# =========================================================================
# Generate tables and figures for the paper 
# Date created: September 18, 2023 
# Date updated: September 23, 2023
# Operating: MacBook Pro  
# Previous File: `bloomberg_attention_v1wrds.R` + `10-X_clean_v2function.R` + `10-X_clean_v3function.R` + `Repurchase_BBAIA_merge_v1.R` > 
# Files: (1) `NEWS_HEAT_READ_DMAX_CUSIP_CIK.csv` from Folder: <NEWS_HEAT_READ_DMAX_CUSIP_CIK.csv>
#        (2) `ShaRep_Russell_Aug28_2023.csv` from Folder: <"~/repurchase_workspace_Aug21_2023/Aug23_2023/10-X_cleaned_Aug23_2023>
# Next File: > `repurchase_merge_v1function.R`
# ======================================================
# Notes: Oct 26, 2023 
# (1) Add CAR measures 
# (2) Add short interest info 
# Notes: Sep 23, 2023 
# (1) Need to update `fe_2sls` and transform a range of variables to the log transformed ones 
# ======================================================

library(zoo)
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library(tidyverse)
## ── Attaching packages
## ───────────────────────────────────────
## tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6     ✔ purrr   0.3.4
## ✔ tibble  3.1.8     ✔ dplyr   1.0.9
## ✔ tidyr   1.2.0     ✔ stringr 1.4.0
## ✔ readr   2.1.2     ✔ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
library(psych)
## 
## Attaching package: 'psych'
## 
## The following objects are masked from 'package:ggplot2':
## 
##     %+%, alpha
library(xtable)
library(stargazer)
## 
## Please cite as: 
## 
##  Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.
##  R package version 5.2.3. https://CRAN.R-project.org/package=stargazer
library(lubridate)
## 
## Attaching package: 'lubridate'
## 
## The following objects are masked from 'package:base':
## 
##     date, intersect, setdiff, union
library(fixest)

## Table 1. su <- ary statistics ---- 
#setwd("~/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/bloomberg_attention_July30_2023_back2023Sept7")
setwd("~/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/tables_code_May04_2024")
list.files()
##  [1] "BB_dt_Sept7_2023.rdata"                        
##  [2] "edcdnnrfzr3ibtln.csv"                          
##  [3] "fig2_attention_hist.png"                       
##  [4] "fig2_attention2.png"                           
##  [5] "fig2_attention3.png"                           
##  [6] "fig2_hist.png"                                 
##  [7] "fig2_hist2.png"                                
##  [8] "NEWS_HEAT_READ_DMAX_CUSIP_CIK_Sept8_2023.rdata"
##  [9] "numerical_solution.R"                          
## [10] "oox7oponsih3x2us.csv"                          
## [11] "pq5ofpjastdmdijh.csv"                          
## [12] "rlvjvxigmhkhctli.csv"                          
## [13] "ShaRep_AIA_CCM_c2_Sept8_2023_BB.rdata"         
## [14] "sharep_cusip_Oct14.txt"                        
## [15] "sharep_cusip_Oct15.txt"                        
## [16] "wbk93yls2qlscvgg.csv"                          
## [17] "writing_tables.html"                           
## [18] "writing_tables.R"                              
## [19] "writing_tables.spin.R"                         
## [20] "writing_tables.spin.Rmd"
### 1.a BBAIA data -----  
load("BB_dt_Sept7_2023.rdata")
names(BB_dt)
## [1] "YM"          "Ticker"      "AIA"         "AIAC"        "ANews"      
## [6] "NewsAverage" "NewsCount"
load(file = "NEWS_HEAT_READ_DMAX_CUSIP_CIK_Sept8_2023.rdata")
BB_dt.linked %>% head
## # A tibble: 6 × 16
##   YM        Ticker     AIA     AIAC ANews NewsA…¹ NewsC…² Marke…³ Market…⁴ CUSIP
##   <yearmon> <chr>    <dbl>    <dbl> <dbl>   <dbl>   <dbl>   <dbl>    <dbl> <chr>
## 1 Jan 2010  A      NaN     NaN       2.35   0.671    28.6 NaN     NaN      0084…
## 2 Feb 2010  A        0.429   0.248   2.5    0.817    44.6   0.925   0.446  0084…
## 3 Mar 2010  A        0.478   0.183   2.30   0.688    38.0   0.861   0.385  0084…
## 4 Apr 2010  A        0.727   0.478   2      0.602    23.6   0.884   0.374  0084…
## 5 May 2010  A        0.476   0.0145  2.33   0.710    28.2   0.400   0.0219 0084…
## 6 Jun 2010  A        0      -0.35    2.23   0.504    30.5   0.670   0.215  0084…
## # … with 6 more variables: Exchange <chr>, Name <chr>, CIK <int>, gvkey <int>,
## #   cusip0 <chr>, CONML <chr>, and abbreviated variable names ¹​NewsAverage,
## #   ²​NewsCount, ³​MarketAIA, ⁴​MarketAIAC
## # ℹ Use `colnames()` to see all variable names
gather(select(BB_dt.linked %>% filter(AIA > 0), AIA, AIAC)) %>%
  na.omit()
## # A tibble: 363,698 × 2
##    key   value
##    <chr> <dbl>
##  1 AIA   0.429
##  2 AIA   0.478
##  3 AIA   0.727
##  4 AIA   0.476
##  5 AIA   1    
##  6 AIA   1.09 
##  7 AIA   1.86 
##  8 AIA   1    
##  9 AIA   1.14 
## 10 AIA   1.43 
## # … with 363,688 more rows
## # ℹ Use `print(n = ...)` to see more rows
### draw the AIA / AIAC histogram -----
ggplot(data = gather(select(BB_dt.linked %>% filter(AIA > 0 & AIA < 4), AIA, AIAC)) %>%
         na.omit()
) + 
  geom_histogram(aes(x = value, fill = key), 
                 colour = 'grey50', alpha = 0.5, position = 'identity') + 
  labs(fill = "Attention", x = NULL, y = NULL) +  # Remove x-axis label
  theme(axis.title.y = element_text(angle = 0, hjust = 0, vjust = 0.1), 
        axis.text = element_text(size = 20), 
        legend.text = element_text(size = 15), 
        legend.title = element_text(size = 18)) # Set y-axis label horizontally at the top
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## 
describe(BB_dt.linked %>% 
           select(AIA, AIAC, ANews, NewsAverage, NewsCount, MarketAIA, MarketAIAC) %>% 
           mutate(AIA = case_when(AIA < 0 ~ 0, AIA >= 0 ~ AIA), 
                  MarketAIA = case_when(MarketAIA < 0 ~ 0, MarketAIA >= 0 ~ MarketAIA)
           ),
         na.rm = T) %>% 
  select(mean, median, sd, min, max, n) %>% 
  mutate(n = as.integer(n)) %>% 
  `colnames<-`(., value = str_to_title(names(.))) %>% 
  xtable()
## % latex table generated in R 4.2.1 by xtable 1.8-4 package
## % Sat May  4 15:07:40 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrrrr}
##   \hline
##  & Mean & Median & Sd & Min & Max & N \\ 
##   \hline
## AIA & 0.71 & 0.45 & 0.78 & 0.00 & 4.00 & 216662 \\ 
##   AIAC & 0.21 & 0.00 & 0.58 & -0.35 & 2.15 & 216632 \\ 
##   ANews & 1.45 & 1.40 & 0.62 & 0.00 & 4.00 & 372735 \\ 
##   NewsAverage & 0.32 & 0.25 & 0.27 & 0.00 & 4.00 & 372735 \\ 
##   NewsCount & 22.05 & 8.43 & 92.59 & 1.00 & 8419.14 & 372175 \\ 
##   MarketAIA & 0.63 & 0.63 & 0.17 & 0.00 & 0.99 & 482444 \\ 
##   MarketAIAC & 0.16 & 0.16 & 0.14 & -0.28 & 0.61 & 482444 \\ 
##    \hline
## \end{tabular}
## \end{table}
hist(BB_dt.linked$NewsCount)

describe(BB_dt %>% 
           select(-YM, -Ticker) %>% 
           mutate(AIA = case_when(AIA < 0 ~ 0, AIA >= 0 ~ AIA)),
         na.rm = T) %>% 
  select(mean, median, sd, min, max, n) %>% 
  mutate(n = as.integer(n)) %>% 
  `colnames<-`(., value = str_to_title(names(.))) %>% 
  xtable()
## % latex table generated in R 4.2.1 by xtable 1.8-4 package
## % Sat May  4 15:07:42 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrrrr}
##   \hline
##  & Mean & Median & Sd & Min & Max & N \\ 
##   \hline
## AIA & 0.71 & 0.45 & 0.78 & 0.00 & 4.00 & 215477 \\ 
##   AIAC & 0.21 & 0.00 & 0.58 & -0.35 & 2.15 & 215447 \\ 
##   ANews & 1.45 & 1.40 & 0.62 & 0.00 & 4.00 & 370798 \\ 
##   NewsAverage & 0.32 & 0.25 & 0.27 & 0.00 & 4.00 & 370798 \\ 
##   NewsCount & 22.03 & 8.41 & 92.67 & 1.00 & 8419.14 & 370238 \\ 
##    \hline
## \end{tabular}
## \end{table}
BB_dt_count <- BB_dt %>% 
  mutate(AIA = case_when(AIA < 0 ~ 0, AIA >= 0 ~ AIA)) %>% 
  select(-Ticker) %>% 
  group_by(YM) %>%
  summarise_all(.funs = function(x) sum(!is.na(x))) %>% 
  ungroup() %>% 
  gather(key = Item, value = 'N', AIA:NewsCount)

BB_dt_sa <- BB_dt %>% 
  mutate(AIA = case_when(AIA < 0 ~ 0, AIA >= 0 ~ AIA)) %>% 
  select(-Ticker) %>% 
  group_by(YM) %>%
  summarise_all(.funs = function(x) mean(x, na.rm = T) ) %>% 
  ungroup() %>% 
  gather(key = Item, value = 'Mean', AIA:NewsCount)


ggplot(BB_dt_count, aes(x = YM, y = N)) +
  geom_line(aes(col = Item))

ggplot(BB_dt_sa, aes(x = YM, y = Mean)) +
  geom_line(aes(col = Item))
## Warning: Removed 2 row(s) containing missing values (geom_path).

plotly::ggplotly(ggplot(BB_dt_count, aes(x = YM, y = N)) +
                   geom_line(aes(col = Item)))
plotly::ggplotly(ggplot(BB_dt_sa, aes(x = YM, y = Mean)) +
  geom_line(aes(col = Item)) )
BB_dt_count %>% group_by(Item) %>% summarise(mean = mean(N, na.rm = T))
## # A tibble: 5 × 2
##   Item         mean
##   <chr>       <dbl>
## 1 AIA         1322.
## 2 AIAC        1322.
## 3 ANews       2275.
## 4 NewsAverage 2275.
## 5 NewsCount   2271.
### 1.b Repurchase Data ----- 
#setwd("~/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/repurchase_merge_Aug29_2023_back2023Sept7")
#load("ShaRep_Russell_Sept7_2023.rdata")
#ShaRep_cleaned_table <- ShaRep_cleaned_table %>% as_tibble
#ShaRep_cleaned_table %>%
#  distinct(cik)
#### import the raw data 
##### share repurchase data in Russell 3000: ~/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/repurchase_workspace_Aug21_2023-2/Aug23_2023/10-X_cleaned_Aug23_2023/10-X_clean_v3function.R
#load("~/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/repurchase_workspace_Aug21_2023-2/Aug23_2023/10-X_cleaned_Aug23_2023/repurchase_cleaned_unit_dvalue_Aug28_2023.rdata")
#repurchase_cleaned_unit_dvalue %>% dim
#names(repurchase_cleaned_unit_dvalue)
#unique(repurchase_cleaned_unit_dvalue$cik) %>% length()
#unique(repurchase_cleaned_unit_dvalue$id) %>% length()

##### all share repurchase data from EDGAR: ~/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/repurchase_workspace_Aug21_2023-2/Aug23_2023/10-X_cleaned_Aug23_2023/10-X_clean_v2bf.R
#load("~/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/repurchase_workspace_Aug21_2023-2/Aug23_2023/10-X_cleaned_Aug23_2023/repurchase_raw2_cleaned_Aug26_2023.rdata")
#repurchase_raw2_cleaned %>% dim
#unique(repurchase_raw2_cleaned$cik) %>% length()
#unique(repurchase_raw2_cleaned$id) %>% length()

##### short interest information: 
short_interest <- read.csv(file = "edcdnnrfzr3ibtln.csv") %>% 
  as_tibble() %>% 
  filter(day(ymd(datadate)) < 20) %>% # choosing the 15th business day of the month 
  mutate(YM = as.yearmon(datadate)) %>% 
  select(YM, gvkey, cusip, sic, shortintadj)
  

## 2. full sample ----
#load("/Users/hongyixu/Library/CloudStorage/OneDrive-HandelshögskolaniStockholm/Projects_2023/Empirical_Design_July18_2023/repurchase_merge_Aug29_2023_back2023Sept7/ShaRep_AIA_CCM_c2_Sept8_2023_BB.rdata")
 load("ShaRep_AIA_CCM_c2_Sept8_2023_BB.rdata") 

#### try to add the number of months after the OMR [May 4, 2024] 
ShaRep_program <- ShaRep_AIA_merge_illiquidity_OMR_CCM_c2 %>% 
  select(YM, gvkey, cusip, OMRFlag) %>% 
  group_by(gvkey, cusip) %>% 
  mutate(OMRIdentifier = cumsum(OMRFlag)) %>% 
  ungroup() # %>% 
# summarise(num = max(OMRIdentifier) - min(OMRIdentifier) + 1) 

  ShaRep_programIDyes <- ShaRep_program %>% filter(OMRFlag == TRUE) %>% select(-OMRFlag) %>% rename(OMR_YM = YM)
  ShaRep_programIDno <- ShaRep_program %>% filter(OMRFlag == FALSE & OMRIdentifier == 0) %>% 
    group_by(gvkey, cusip, OMRIdentifier) %>% 
    summarise(OMR_YM = min(YM)) %>% 
    ungroup() %>% 
    select(OMR_YM, gvkey, cusip, OMRIdentifier)
## `summarise()` has grouped output by 'gvkey', 'cusip'. You can override using
## the `.groups` argument.
  ShaRep_programID <- rbind.data.frame(ShaRep_programIDyes, ShaRep_programIDno)
  
  ShaRep_programmonth <- ShaRep_program %>% 
    left_join(ShaRep_programID, by = c("gvkey", "cusip", "OMRIdentifier") )

ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary <- ShaRep_AIA_merge_illiquidity_OMR_CCM_c2 %>% 
  left_join(short_interest, by = c('YM', 'gvkey', 'cusip')) %>% # append the short interest data 
  left_join(select(ShaRep_programmonth, YM, gvkey, cusip, OMR_YM), by = c('YM', 'gvkey', 'cusip')) %>% 
  # mutate(EBITDAtA = EBITDA / TA) %>% 
  mutate(ShaRep3 = ShaRep3 / 10^6, 
         ShaOut = ShaOut / 10^6, 
         MarCap = MarCap / 10^6, 
         TradeVol = TradeVol / 10^6 , 
         TradeVolDollar = TradeVolDollar / 10^6, 
         OMRFlag = as.numeric(OMRFlag), 
         # BM = BM*10^6, 
         Amihud_monthly = Amihud_monthly, 
         ShaRepYes = as.numeric(ShaRepYes), 
         ProgramMonth = 1 + 12 * (YM - OMR_YM), # the number of months passed after the OMR announcement. (The first (announcement) month is 1 (not 0)). [May 4, 2024]
         ShortInterest = shortintadj / ShaOutPrevious # short interest at 15th of the month / last month share outstanding. 
         ) # %>% 
  #left_join(select(repurchase_cleaned_unit_dvalue, period_ym, cik, reporting, filing) %>% 
  #            distinct %>% 
  #            group_by(period_ym, cik) %>% 
  #            filter(filing == min(filing)) %>% ungroup() %>% 
  #            mutate(cik = as.numeric(cik)), by = c('YM' = 'period_ym', 'CIK' = 'cik') )


ShaRep_CAR_txt <- ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% 
  mutate(ymd = as.Date(YM, frac = 1) %>% as.character ) %>% 
  select(CUSIP, ymd) 

# write.table(x = ShaRep_CAR_txt, file = "sharep_cusip_Oct14.txt", col.names = F, row.names = F, quote = F)
#### 2.1 clean and store the CAR for 3- and 6-months  ======
{ # plug "sharep_cusip_Oct14.txt" into WRDS: 
  sharep_car6 <- read.csv(file = "pq5ofpjastdmdijh.csv") %>% 
    as_tibble() %>% 
    mutate(YM = as.yearmon(original_da_date)) %>% 
    select(YM, cusip, wv_bhar_reb6 = wv_bhar_reb, wv_bhar_nreb6 = wv_bhar_nreb) 
  sharep_car3 <- read.csv(file = "wbk93yls2qlscvgg.csv") %>% 
    as_tibble() %>% 
    mutate(YM = as.yearmon(original_da_date)) %>% 
    select(YM, cusip, wv_bhar_reb3 = wv_bhar_reb, wv_bhar_nreb3 = wv_bhar_nreb) 
  sharep_car1 <- read.csv(file = "oox7oponsih3x2us.csv") %>% 
    as_tibble() %>% 
    mutate(YM = as.yearmon(original_da_date)) %>% 
    select(YM, cusip, wv_bhar_reb1 = wv_bhar_reb, wv_bhar_nreb1 = wv_bhar_nreb) 
  # plug "sharep_cusip_Oct15.txt" into WRDS: 
  sharep_car0 <- read.csv(file = "rlvjvxigmhkhctli.csv") %>% 
    as_tibble() %>% 
    mutate(YM = as.yearmon(original_da_date) + 1/12) %>% 
    select(YM, cusip, wv_bhar_reb0 = wv_bhar_reb, wv_bhar_nreb0 = wv_bhar_nreb) 
  
  sharep_car <- sharep_car3 %>% 
    left_join(sharep_car6, by = c('YM', 'cusip')) %>% 
    left_join(sharep_car1, by = c('YM', 'cusip')) %>% 
    left_join(sharep_car0, by = c('YM', 'cusip')) %>% 
    mutate_at(vars(contains("reb")), .funs = function(x) as.numeric(gsub(pattern = "%", replacement = "", x)))
}

#### 2.2 append the CAR for 3- and 6-months  ======
ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary <- ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% 
  left_join(sharep_car, by = c('YM', 'CUSIP' = 'cusip'))


ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% names
##  [1] "YM"               "AIAC"             "ANews"            "NewsAverage"     
##  [5] "NewsCount"        "MarketAIA"        "MarketAIAC"       "CUSIP"           
##  [9] "CIK"              "gvkey"            "Name"             "cusip8"          
## [13] "CUSIP_tts"        "AIA"              "ShaRep3"          "missing3"        
## [17] "Price2"           "Amihud_monthly"   "OMRFlag"          "Ticker"          
## [21] "RET_m1"           "Volatility"       "AvePrice"         "TradeVol"        
## [25] "TradeVolDollar"   "MarCap"           "ShaOut"           "ShaOutPrevious"  
## [29] "datadate"         "tic"              "cusip"            "atq"             
## [33] "ceqq"             "cheq"             "oibdpq"           "pstkq"           
## [37] "seqq"             "txditcq"          "cdvcy"            "costat"          
## [41] "dlcq"             "dlttq"            "BE"               "TD"              
## [45] "CtA"              "TA"               "Year"             "Quarter"         
## [49] "Month"            "RepIntensity"     "RepIntensity_vol" "ShaRepYes"       
## [53] "BM"               "DivtoAsset"       "EBITDA"           "Leverage"        
## [57] "TradeVol_scaled"  "EBITDAtA"         "time"             "sic"             
## [61] "shortintadj"      "OMR_YM"           "ProgramMonth"     "ShortInterest"   
## [65] "wv_bhar_reb3"     "wv_bhar_nreb3"    "wv_bhar_reb6"     "wv_bhar_nreb6"   
## [69] "wv_bhar_reb1"     "wv_bhar_nreb1"    "wv_bhar_reb0"     "wv_bhar_nreb0"
tbl1_cleaned <- tbl1 <- describe(ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% 
           # select(-c(YM, CUSIP, CIK, gvkey, Name, cusip8, cusip, datadate, time,
           #         missing3, ShaRepYes, UnderPriced, 
           #         CUSIP_tts, tic, Ticker)) %>% 
           select(ShaRep3, RepIntensity, RepIntensity_vol, 
                  Amihud_monthly, BM, AvePrice, CtA, DivtoAsset, EBITDAtA, TA, 
                  Leverage, MarCap, OMRFlag, RET_m1, TradeVol, TradeVol_scaled, Volatility, ShaRepYes
                  ) , 
         na.rm = T) %>% 
  select(mean, median, sd, min, max, n) %>% 
  mutate(n = as.integer(n)) %>% 
  `colnames<-`(., value = str_to_title(names(.))) 

tbl1_cleaned[c("RepIntensity", "RepIntensity_vol"),1:5] <-
  tbl1[c("RepIntensity", "RepIntensity_vol"),1:5] * 10^2

tbl1_cleaned[c("DivtoAsset"),1:5] * 10^2
##                  Mean Median        Sd Min      Max
## DivtoAsset 0.02696258      0 0.2164935   0 10.50881
tbl1_cleaned %>% 
  # format(digits = 2)
  xtable()
## % latex table generated in R 4.2.1 by xtable 1.8-4 package
## % Sat May  4 15:08:26 2024
## \begin{table}[ht]
## \centering
## \begin{tabular}{rrrrrrr}
##   \hline
##  & Mean & Median & Sd & Min & Max & N \\ 
##   \hline
## ShaRep3 & 1.04 & 0.00 & 4.47 & 0.00 & 266.40 & 73926 \\ 
##   RepIntensity & 0.31 & 0.00 & 0.81 & 0.00 & 44.47 & 73851 \\ 
##   RepIntensity\_vol & 1.84 & 0.00 & 5.51 & 0.00 & 546.44 & 73926 \\ 
##   Amihud\_monthly & 0.00 & 0.00 & 0.01 & 0.00 & 1.27 & 73926 \\ 
##   BM & 0.48 & 0.38 & 0.53 & -12.95 & 25.01 & 73383 \\ 
##   AvePrice & 78.28 & 50.41 & 144.88 & 0.17 & 5191.13 & 73926 \\ 
##   CtA & 0.14 & 0.09 & 0.14 & 0.00 & 1.00 & 73383 \\ 
##   DivtoAsset & 0.00 & 0.00 & 0.00 & 0.00 & 0.11 & 73383 \\ 
##   EBITDAtA & 0.03 & 0.03 & 0.03 & -0.90 & 0.48 & 73383 \\ 
##   TA & 37726.95 & 6544.53 & 156608.01 & 26.58 & 3213115.00 & 73383 \\ 
##   Leverage & 0.39 & 0.34 & 0.25 & 0.00 & 0.99 & 73383 \\ 
##   MarCap & 23570.90 & 6389.77 & 66815.58 & 8.39 & 2447988.71 & 73926 \\ 
##   OMRFlag & 0.02 & 0.00 & 0.15 & 0.00 & 1.00 & 73926 \\ 
##   RET\_m1 & 0.01 & 0.01 & 0.12 & -0.85 & 16.25 & 73906 \\ 
##   TradeVol & 55.78 & 23.65 & 111.94 & 0.00 & 3881.63 & 73926 \\ 
##   TradeVol\_scaled & 0.20 & 0.16 & 0.23 & -0.23 & 18.10 & 73851 \\ 
##   Volatility & 0.02 & 0.02 & 0.01 & 0.00 & 0.79 & 73921 \\ 
##   ShaRepYes & 0.52 & 1.00 & 0.50 & 0.00 & 1.00 & 73926 \\ 
##    \hline
## \end{tabular}
## \end{table}
## Table 3. OLS ----- 

pdShaRep <- panel(ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% 
                    # mutate(reporting_ym = as.yearmon(reporting), 
                    #        filing_ym = as.yearmon(filing)) %>% 
                    filter(RepIntensity <= 0.10) %>% 
                    mutate(TradeVol_shaout = TradeVol / ShaOut) %>% 
                    group_by(YM) %>% 
                    mutate(BM_q1 = quantile(BM, na.rm = T)[2],
                           BM_q2 = quantile(BM, na.rm = T)[3],
                           BM_q3 = quantile(BM, na.rm = T)[4],
                           BM_q4 = quantile(BM, na.rm = T)[5],
                           RET_md = median(RET_m1, na.rm = T), 
                           RET_mean = mean(RET_m1, na.rm = T), 
                           frequency = mean(ShaRepYes, na.rm = T),
                           Volatility_md = median(Volatility, na.rm = T)
                    ) %>% 
                    ungroup() %>% 
                    mutate(UnderPriced = BM > BM_q2,
                           BM_middle = (BM >= BM_q1) & (BM <= BM_q3) ,
                           PriceQ1 = 1*(BM <= BM_q1), 
                           PriceQ2 = 2*(BM > BM_q1 & BM <= BM_q2), 
                           PriceQ3 = 3*(BM > BM_q2 & BM <= BM_q3), 
                           PriceQ4 = 4*(BM > BM_q3 & BM <= BM_q4), 
                           PriceQ = PriceQ1 + PriceQ2 + PriceQ3 + PriceQ4, 
                           HighVolatility = Volatility > Volatility_md, 
                           RET_m1_0 = RET_m1 > 0, 
                    ) %>% 
                    mutate(YQ = yearqtr(YM))# %>% 
                  #mutate(group1 = (wv_bhar_reb1 > 0) + (wv_bhar_reb0 > 0), 
                  #       group3 = (wv_bhar_reb3 > 0) + (wv_bhar_reb0 > 0),
                  #       group6 = (wv_bhar_reb6 > 0) + (wv_bhar_reb0 > 0)
                  # )
                  , ~ Ticker + time)
names(pdShaRep)
##  [1] "YM"               "AIAC"             "ANews"            "NewsAverage"     
##  [5] "NewsCount"        "MarketAIA"        "MarketAIAC"       "CUSIP"           
##  [9] "CIK"              "gvkey"            "Name"             "cusip8"          
## [13] "CUSIP_tts"        "AIA"              "ShaRep3"          "missing3"        
## [17] "Price2"           "Amihud_monthly"   "OMRFlag"          "Ticker"          
## [21] "RET_m1"           "Volatility"       "AvePrice"         "TradeVol"        
## [25] "TradeVolDollar"   "MarCap"           "ShaOut"           "ShaOutPrevious"  
## [29] "datadate"         "tic"              "cusip"            "atq"             
## [33] "ceqq"             "cheq"             "oibdpq"           "pstkq"           
## [37] "seqq"             "txditcq"          "cdvcy"            "costat"          
## [41] "dlcq"             "dlttq"            "BE"               "TD"              
## [45] "CtA"              "TA"               "Year"             "Quarter"         
## [49] "Month"            "RepIntensity"     "RepIntensity_vol" "ShaRepYes"       
## [53] "BM"               "DivtoAsset"       "EBITDA"           "Leverage"        
## [57] "TradeVol_scaled"  "EBITDAtA"         "time"             "sic"             
## [61] "shortintadj"      "OMR_YM"           "ProgramMonth"     "ShortInterest"   
## [65] "wv_bhar_reb3"     "wv_bhar_nreb3"    "wv_bhar_reb6"     "wv_bhar_nreb6"   
## [69] "wv_bhar_reb1"     "wv_bhar_nreb1"    "wv_bhar_reb0"     "wv_bhar_nreb0"   
## [73] "TradeVol_shaout"  "BM_q1"            "BM_q2"            "BM_q3"           
## [77] "BM_q4"            "RET_md"           "RET_mean"         "frequency"       
## [81] "Volatility_md"    "UnderPriced"      "BM_middle"        "PriceQ1"         
## [85] "PriceQ2"          "PriceQ3"          "PriceQ4"          "PriceQ"          
## [89] "HighVolatility"   "RET_m1_0"         "YQ"
#### 3.1 RepIntensity -----
#### with AIA # updated September 22, 2023 
RepInt_ols1 <- feols(fml = RepIntensity ~ AIA + l(RepIntensity, 1) + 
        log(Amihud_monthly) + OMRFlag + l(RET_m1, 1:3)
      | Ticker + time , # + Ticker^yearqtr(YM),
      data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
      cluster = c("Ticker"))
## NOTE: 32,055 observations removed because of NA values (RHS: 32,055).
summary(RepInt_ols1)
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 41,730 
## Fixed-effects: Ticker: 1,268,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error  t value   Pr(>|t|)    
## AIA                 -0.000575   0.000099 -5.79166 8.7811e-09 ***
## l(RepIntensity, 1)   0.178146   0.022932  7.76855 1.6306e-14 ***
## log(Amihud_monthly) -0.000913   0.000096 -9.50489  < 2.2e-16 ***
## OMRFlag              0.001625   0.000281  5.78256 9.2567e-09 ***
## l(RET_m1, 1)        -0.003692   0.000451 -8.18406 6.6215e-16 ***
## l(RET_m1, 2)        -0.002160   0.000387 -5.58595 2.8418e-08 ***
## l(RET_m1, 3)        -0.001292   0.000367 -3.52064 4.4578e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005517     Adj. R2: 0.220536
##                  Within R2: 0.044414
RepInt_ols2 <- feols(fml = RepIntensity ~ AIA + l(RepIntensity, 1) +
        log(Amihud_monthly) + OMRFlag + 
        l(RET_m1, 1:3) + log(TA) + (CtA) + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
        l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) 
        | Ticker + time, # + Ticker^yearqtr(YM), # + Ticker^Year,
      data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
      cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 33,949 observations removed because of NA and infinite values (RHS: 33,949).
summary(RepInt_ols2)
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 39,836 
## Fixed-effects: Ticker: 1,237,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## AIA                 -0.000606   0.000100  -6.068851 1.7107e-09 ***
## l(RepIntensity, 1)   0.176948   0.024295   7.283258 5.7862e-13 ***
## log(Amihud_monthly) -0.002067   0.000148 -13.936154  < 2.2e-16 ***
## OMRFlag              0.001634   0.000293   5.566323 3.1879e-08 ***
## l(RET_m1, 1)        -0.004014   0.000475  -8.455838  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001539   0.000391  -3.933056 8.8534e-05 ***
## l(RET_m1, 3)        -0.000621   0.000371  -1.675381 9.4112e-02 .  
## log(TA)             -0.000874   0.000416  -2.100009 3.5930e-02 *  
## CtA                  0.002064   0.000799   2.581637 9.9476e-03 ** 
## EBITDAtA             0.004833   0.002626   1.840592 6.5921e-02 .  
## Leverage             0.000229   0.001452   0.157515 8.7486e-01    
## log(BM)              0.000928   0.000140   6.640155 4.6815e-11 ***
## DivtoAsset          -0.007557   0.017767  -0.425352 6.7065e-01    
## l(log(MarCap), 1)   -0.001203   0.000383  -3.137677 1.7432e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230906
##                  Within R2: 0.056297
RepInt_ols3 <- feols(fml = RepIntensity ~ AIA + l(RepIntensity, 1) +
        log(Amihud_monthly) + OMRFlag + 
        l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
        l(log(MarCap), 1) + # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) + # l(log(TradeVol), 0:1)
        ANews + NewsAverage + log(NewsCount) + ShortInterest + d(ShortInterest,1)
      | Ticker + time , #+ Ticker^YQ , # + Ticker^Year,
      data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
      cluster = "Ticker")
## Warning in log(BM): NaNs produced
## NOTE: 34,679 observations removed because of NA and infinite values (RHS: 34,679).
summary(RepInt_ols3)
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 39,106 
## Fixed-effects: Ticker: 1,216,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## AIA                 -0.000524   0.000100  -5.237942 1.9124e-07 ***
## l(RepIntensity, 1)   0.173905   0.024639   7.058087 2.8310e-12 ***
## log(Amihud_monthly) -0.002080   0.000153 -13.567421  < 2.2e-16 ***
## OMRFlag              0.001622   0.000302   5.376286 9.1109e-08 ***
## l(RET_m1, 1)        -0.003798   0.000482  -7.875427 7.4844e-15 ***
## l(RET_m1, 2)        -0.001370   0.000409  -3.348097 8.3861e-04 ***
## l(RET_m1, 3)        -0.000525   0.000374  -1.403379 1.6076e-01    
## log(TA)             -0.000838   0.000440  -1.906006 5.6885e-02 .  
## CtA                  0.001891   0.000766   2.467321 1.3750e-02 *  
## EBITDAtA             0.005294   0.002907   1.820923 6.8864e-02 .  
## Leverage             0.000075   0.001499   0.050180 9.5999e-01    
## log(BM)              0.000928   0.000139   6.667482 3.9400e-11 ***
## DivtoAsset          -0.007896   0.017840  -0.442632 6.5811e-01    
## l(log(MarCap), 1)   -0.001254   0.000393  -3.187190 1.4732e-03 ** 
## ANews               -0.000525   0.000155  -3.387819 7.2707e-04 ***
## NewsAverage          0.000170   0.000341   0.499205 6.1773e-01    
## log(NewsCount)       0.000086   0.000103   0.843047 3.9937e-01    
## ShortInterest       -0.000685   0.001077  -0.636060 5.2486e-01    
## d(ShortInterest, 1)  0.017957   0.006101   2.943102 3.3111e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005412     Adj. R2: 0.232359
##                  Within R2: 0.059071
#### with AIAC  
{# now with AIAC 
  RepInt_ols1a <- feols(fml = RepIntensity ~ AIAC + l(RepIntensity, 1) + 
                         log(Amihud_monthly) + OMRFlag + l(RET_m1, 1:3)
                       | Ticker + time , # + Ticker^yearqtr(YM),
                       data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                       cluster = c("Ticker"))
  RepInt_ols1a
  
  RepInt_ols2a <- feols(fml = RepIntensity ~ AIAC + l(RepIntensity, 1) +
                         log(Amihud_monthly) + OMRFlag + 
                         l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                         l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + log(TradeVol) # + 
                       # ANews + NewsAverage + NewsCount
                       | Ticker + time , # + Ticker^Year,
                       data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                       cluster = c("Ticker"))
  RepInt_ols2a
  
  RepInt_ols3a <- feols(fml = RepIntensity ~ AIAC + l(RepIntensity, 1) +
                         log(Amihud_monthly) + OMRFlag + 
                         l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                         l(log(MarCap), 1) + # d(Volatility,1) + l(Volatility, 1) + log(TradeVol) + 
                         ANews + NewsAverage + log(NewsCount)
                       | Ticker + time , # + Ticker^Year,
                       data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                       cluster = c("Ticker"))
  summary(RepInt_ols3a)
}
## NOTE: 32,055 observations removed because of NA values (RHS: 32,055).
## Warning in log(BM): NaNs produced
## NOTE: 33,949 observations removed because of NA and infinite values (RHS: 33,949).
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## AIAC                -0.000747   0.000152  -4.925138 9.5799e-07 ***
## l(RepIntensity, 1)   0.175750   0.024374   7.210686 9.7058e-13 ***
## log(Amihud_monthly) -0.002079   0.000150 -13.864127  < 2.2e-16 ***
## OMRFlag              0.001647   0.000297   5.544518 3.6055e-08 ***
## l(RET_m1, 1)        -0.003997   0.000478  -8.359415  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001574   0.000397  -3.967613 7.6797e-05 ***
## l(RET_m1, 3)        -0.000585   0.000373  -1.567984 1.1714e-01    
## log(TA)             -0.000847   0.000421  -2.010562 4.4590e-02 *  
## CtA                  0.001766   0.000763   2.312816 2.0897e-02 *  
## EBITDAtA             0.005015   0.002839   1.766529 7.7555e-02 .  
## Leverage             0.000159   0.001460   0.108954 9.1326e-01    
## log(BM)              0.000946   0.000139   6.823902 1.3882e-11 ***
## DivtoAsset          -0.009577   0.017958  -0.533296 5.9393e-01    
## l(log(MarCap), 1)   -0.001173   0.000386  -3.036421 2.4445e-03 ** 
## ANews               -0.000525   0.000155  -3.377167 7.5529e-04 ***
## NewsAverage          0.000086   0.000347   0.246650 8.0522e-01    
## log(NewsCount)       0.000111   0.000103   1.081014 2.7990e-01    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230793
##                  Within R2: 0.056916
etable(RepInt_ols1, RepInt_ols2, RepInt_ols3,
       RepInt_ols1a, RepInt_ols2a, RepInt_ols3a,
       # vcov = "Ticker", 
       # headers = paste("(", 1:3, ")", sep = ""),
       tex = T)
## \begingroup
## \centering
## \begin{tabular}{lcccccc}
##    \tabularnewline \midrule \midrule
##    Dependent Variable: & \multicolumn{6}{c}{RepIntensity}\\
##    Model:                & (1)                     & (2)                     & (3)                   & (4)                     & (5)             & (6)\\  
##    \midrule
##    \emph{Variables}\\
##    AIA                   & -0.0006$^{***}$         & -0.0006$^{***}$         & -0.0005$^{***}$       &                         &                 &   \\   
##                          & ($9.93\times 10^{-5}$)  & ($9.98\times 10^{-5}$)  & (0.0001)              &                         &                 &   \\   
##    l(RepIntensity,1)     & 0.1781$^{***}$          & 0.1769$^{***}$          & 0.1739$^{***}$        & 0.1781$^{***}$          & 0.1769$^{***}$  & 0.1758$^{***}$\\   
##                          & (0.0229)                & (0.0243)                & (0.0246)              & (0.0229)                & (0.0243)        & (0.0244)\\   
##    log(Amihud\_monthly)  & -0.0009$^{***}$         & -0.0021$^{***}$         & -0.0021$^{***}$       & -0.0009$^{***}$         & -0.0021$^{***}$ & -0.0021$^{***}$\\   
##                          & ($9.6\times 10^{-5}$)   & (0.0001)                & (0.0002)              & ($9.67\times 10^{-5}$)  & (0.0001)        & (0.0001)\\   
##    OMRFlag               & 0.0016$^{***}$          & 0.0016$^{***}$          & 0.0016$^{***}$        & 0.0016$^{***}$          & 0.0016$^{***}$  & 0.0016$^{***}$\\   
##                          & (0.0003)                & (0.0003)                & (0.0003)              & (0.0003)                & (0.0003)        & (0.0003)\\   
##    l(RET\_m1,1)          & -0.0037$^{***}$         & -0.0040$^{***}$         & -0.0038$^{***}$       & -0.0037$^{***}$         & -0.0040$^{***}$ & -0.0040$^{***}$\\   
##                          & (0.0005)                & (0.0005)                & (0.0005)              & (0.0005)                & (0.0005)        & (0.0005)\\   
##    l(RET\_m1,2)          & -0.0022$^{***}$         & -0.0015$^{***}$         & -0.0014$^{***}$       & -0.0022$^{***}$         & -0.0016$^{***}$ & -0.0016$^{***}$\\   
##                          & (0.0004)                & (0.0004)                & (0.0004)              & (0.0004)                & (0.0004)        & (0.0004)\\   
##    l(RET\_m1,3)          & -0.0013$^{***}$         & -0.0006$^{*}$           & -0.0005               & -0.0013$^{***}$         & -0.0006$^{*}$   & -0.0006\\   
##                          & (0.0004)                & (0.0004)                & (0.0004)              & (0.0004)                & (0.0004)        & (0.0004)\\   
##    log(TA)               &                         & -0.0009$^{**}$          & -0.0008$^{*}$         &                         & -0.0009$^{**}$  & -0.0008$^{**}$\\   
##                          &                         & (0.0004)                & (0.0004)              &                         & (0.0004)        & (0.0004)\\   
##    CtA                   &                         & 0.0021$^{***}$          & 0.0019$^{**}$         &                         & 0.0021$^{***}$  & 0.0018$^{**}$\\   
##                          &                         & (0.0008)                & (0.0008)              &                         & (0.0008)        & (0.0008)\\   
##    EBITDAtA              &                         & 0.0048$^{*}$            & 0.0053$^{*}$          &                         & 0.0048$^{*}$    & 0.0050$^{*}$\\   
##                          &                         & (0.0026)                & (0.0029)              &                         & (0.0026)        & (0.0028)\\   
##    Leverage              &                         & 0.0002                  & $7.52\times 10^{-5}$  &                         & 0.0003          & 0.0002\\   
##                          &                         & (0.0015)                & (0.0015)              &                         & (0.0015)        & (0.0015)\\   
##    log(BM)               &                         & 0.0009$^{***}$          & 0.0009$^{***}$        &                         & 0.0009$^{***}$  & 0.0009$^{***}$\\   
##                          &                         & (0.0001)                & (0.0001)              &                         & (0.0001)        & (0.0001)\\   
##    DivtoAsset            &                         & -0.0076                 & -0.0079               &                         & -0.0080         & -0.0096\\   
##                          &                         & (0.0178)                & (0.0178)              &                         & (0.0179)        & (0.0180)\\   
##    l(log(MarCap),1)      &                         & -0.0012$^{***}$         & -0.0013$^{***}$       &                         & -0.0012$^{***}$ & -0.0012$^{***}$\\   
##                          &                         & (0.0004)                & (0.0004)              &                         & (0.0004)        & (0.0004)\\   
##    ANews                 &                         &                         & -0.0005$^{***}$       &                         &                 & -0.0005$^{***}$\\   
##                          &                         &                         & (0.0002)              &                         &                 & (0.0002)\\   
##    NewsAverage           &                         &                         & 0.0002                &                         &                 & $8.55\times 10^{-5}$\\    
##                          &                         &                         & (0.0003)              &                         &                 & (0.0003)\\   
##    log(NewsCount)        &                         &                         & $8.64\times 10^{-5}$  &                         &                 & 0.0001\\   
##                          &                         &                         & (0.0001)              &                         &                 & (0.0001)\\   
##    ShortInterest         &                         &                         & -0.0007               &                         &                 &   \\   
##                          &                         &                         & (0.0011)              &                         &                 &   \\   
##    d(ShortInterest,1)    &                         &                         & 0.0180$^{***}$        &                         &                 &   \\   
##                          &                         &                         & (0.0061)              &                         &                 &   \\   
##    AIAC                  &                         &                         &                       & -0.0008$^{***}$         & -0.0009$^{***}$ & -0.0007$^{***}$\\   
##                          &                         &                         &                       & (0.0001)                & (0.0001)        & (0.0002)\\   
##    \midrule
##    \emph{Fixed-effects}\\
##    Ticker                & Yes                     & Yes                     & Yes                   & Yes                     & Yes             & Yes\\  
##    time                  & Yes                     & Yes                     & Yes                   & Yes                     & Yes             & Yes\\  
##    \midrule
##    \emph{Fit statistics}\\
##    Observations          & 41,730                  & 39,836                  & 39,106                & 41,730                  & 39,836          & 39,470\\  
##    R$^2$                 & 0.24622                 & 0.25699                 & 0.25857               & 0.24623                 & 0.25702         & 0.25703\\  
##    Within R$^2$          & 0.04441                 & 0.05630                 & 0.05907               & 0.04442                 & 0.05634         & 0.05692\\  
##    \midrule \midrule
##    \multicolumn{7}{l}{\emph{Clustered (Ticker) standard-errors in parentheses}}\\
##    \multicolumn{7}{l}{\emph{Signif. Codes: ***: 0.01, **: 0.05, *: 0.1}}\\
## \end{tabular}
## \par\endgroup
#### 3.2 RepIntensity_vol -----
RepIntVol_ols1 <- feols(fml = RepIntensity_vol ~ AIA + l(RepIntensity_vol, 1) + 
                          log(Amihud_monthly) + OMRFlag + l(RET_m1, 1:3)
                     | Ticker + time , # + Ticker^yearqtr(YM),
                     data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                     cluster = c("Ticker"))
## NOTE: 32,055 observations removed because of NA values (RHS: 32,055).
RepIntVol_ols1
## OLS estimation, Dep. Var.: RepIntensity_vol
## Observations: 41,730 
## Fixed-effects: Ticker: 1,268,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error  t value   Pr(>|t|)    
## AIA                    -0.005227   0.000531 -9.85006  < 2.2e-16 ***
## l(RepIntensity_vol, 1)  0.204657   0.035086  5.83305 6.9012e-09 ***
## log(Amihud_monthly)    -0.001991   0.000461 -4.32217 1.6660e-05 ***
## OMRFlag                 0.007098   0.001532  4.63412 3.9545e-06 ***
## l(RET_m1, 1)           -0.010433   0.001772 -5.88753 5.0144e-09 ***
## l(RET_m1, 2)           -0.005111   0.001617 -3.16167 1.6059e-03 ** 
## l(RET_m1, 3)           -0.001731   0.001546 -1.11978 2.6302e-01    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.029142     Adj. R2: 0.259332
##                  Within R2: 0.049006
RepIntVol_ols2 <- feols(fml = RepIntensity_vol ~ AIA + l(RepIntensity_vol, 1) +  
                       log(Amihud_monthly) + OMRFlag + 
                       l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                       l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + log(TradeVol) # + 
                     # ANews + NewsAverage + NewsCount
                     | Ticker + time , # + Ticker^Year,
                     data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                     cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 33,949 observations removed because of NA and infinite values (RHS: 33,949).
RepIntVol_ols2
## OLS estimation, Dep. Var.: RepIntensity_vol
## Observations: 39,836 
## Fixed-effects: Ticker: 1,237,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error   t value   Pr(>|t|)    
## AIA                    -0.005290   0.000540 -9.797665  < 2.2e-16 ***
## l(RepIntensity_vol, 1)  0.204719   0.037161  5.508931 4.3887e-08 ***
## log(Amihud_monthly)    -0.003926   0.000741 -5.297871 1.3860e-07 ***
## OMRFlag                 0.007063   0.001603  4.406557 1.1413e-05 ***
## l(RET_m1, 1)           -0.012041   0.001936 -6.220718 6.7606e-10 ***
## l(RET_m1, 2)           -0.003203   0.001636 -1.957818 5.0476e-02 .  
## l(RET_m1, 3)            0.000216   0.001619  0.133216 8.9404e-01    
## log(TA)                 0.000591   0.001973  0.299439 7.6466e-01    
## CtA                     0.014256   0.004116  3.463897 5.5063e-04 ***
## EBITDAtA                0.010498   0.011020  0.952598 3.4098e-01    
## Leverage               -0.018310   0.007050 -2.597105 9.5129e-03 ** 
## log(BM)                 0.003289   0.000680  4.837162 1.4829e-06 ***
## DivtoAsset             -0.069392   0.103978 -0.667376 5.0466e-01    
## l(log(MarCap), 1)      -0.004146   0.001840 -2.253799 2.4383e-02 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.028965     Adj. R2: 0.264714
##                  Within R2: 0.053432
RepIntVol_ols3 <- feols(fml = RepIntensity_vol ~ AIA + l(RepIntensity_vol, 1) +  
                       log(Amihud_monthly) + OMRFlag + 
                       l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                       l(log(MarCap), 1) + # d(Volatility,1) + l(Volatility, 1) + log(TradeVol) + 
                       ANews + NewsAverage + log(NewsCount)
                     | Ticker + time , # + Ticker^Year,
                     data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                     cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
summary(RepIntVol_ols3)
## OLS estimation, Dep. Var.: RepIntensity_vol
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error   t value   Pr(>|t|)    
## AIA                    -0.003871   0.000538 -7.189933 1.1232e-12 ***
## l(RepIntensity_vol, 1)  0.202562   0.037373  5.420030 7.1670e-08 ***
## log(Amihud_monthly)    -0.004548   0.000740 -6.144700 1.0808e-09 ***
## OMRFlag                 0.007716   0.001614  4.780240 1.9624e-06 ***
## l(RET_m1, 1)           -0.012096   0.001967 -6.148069 1.0587e-09 ***
## l(RET_m1, 2)           -0.003259   0.001656 -1.967342 4.9369e-02 *  
## l(RET_m1, 3)            0.000400   0.001634  0.244701 8.0673e-01    
## log(TA)                 0.000777   0.002002  0.388053 6.9804e-01    
## CtA                     0.013133   0.003997  3.285332 1.0474e-03 ** 
## EBITDAtA                0.009382   0.011922  0.786902 4.3149e-01    
## Leverage               -0.018156   0.007097 -2.558361 1.0636e-02 *  
## log(BM)                 0.003343   0.000681  4.908441 1.0415e-06 ***
## DivtoAsset             -0.069555   0.108842 -0.639045 5.2291e-01    
## l(log(MarCap), 1)      -0.004245   0.001867 -2.273896 2.3144e-02 *  
## ANews                  -0.001105   0.000796 -1.388062 1.6537e-01    
## NewsAverage            -0.002372   0.001582 -1.499861 1.3391e-01    
## log(NewsCount)         -0.002199   0.000563 -3.904652 9.9494e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.028979     Adj. R2: 0.266223
##                  Within R2: 0.055695
#### with AIAC  
{# now with AIAC 
  RepIntVol_ols1a <- feols(fml = RepIntensity_vol ~ AIAC + l(RepIntensity_vol, 1) + 
                             log(Amihud_monthly) + OMRFlag + l(RET_m1, 1:3)
                        | Ticker + time , # + Ticker^yearqtr(YM),
                        data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                        cluster = c("Ticker"))
  RepIntVol_ols1a
  
  RepIntVol_ols2a <- feols(fml = RepIntensity_vol ~ AIAC + l(RepIntensity_vol, 1) + 
                          log(Amihud_monthly) + OMRFlag + 
                          l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                          l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + log(TradeVol) # + 
                        # ANews + NewsAverage + NewsCount
                        | Ticker + time , # + Ticker^Year,
                        data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                        cluster = c("Ticker"))
  RepIntVol_ols2a
  
  RepIntVol_ols3a <- feols(fml = RepIntensity_vol ~ AIAC + l(RepIntensity_vol, 1) + 
                          log(Amihud_monthly) + OMRFlag + 
                          l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                          l(log(MarCap), 1) + # d(Volatility,1) + l(Volatility, 1) + log(TradeVol) + 
                          ANews + NewsAverage + log(NewsCount)
                        | Ticker + time, # + Ticker^yearqtr(YM), # + Ticker^Year,
                        data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
                        cluster = c("Ticker"))
  summary(RepIntVol_ols3a)
}
## NOTE: 32,055 observations removed because of NA values (RHS: 32,055).
## Warning in log(BM): NaNs produced
## NOTE: 33,949 observations removed because of NA and infinite values (RHS: 33,949).
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
## OLS estimation, Dep. Var.: RepIntensity_vol
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error   t value   Pr(>|t|)    
## AIAC                   -0.005692   0.000792 -7.189856 1.1238e-12 ***
## l(RepIntensity_vol, 1)  0.202327   0.037366  5.414815 7.3740e-08 ***
## log(Amihud_monthly)    -0.004633   0.000739 -6.267579 5.0661e-10 ***
## OMRFlag                 0.007700   0.001615  4.766996 2.0934e-06 ***
## l(RET_m1, 1)           -0.012112   0.001969 -6.151820 1.0347e-09 ***
## l(RET_m1, 2)           -0.003346   0.001657 -2.019091 4.3695e-02 *  
## l(RET_m1, 3)            0.000287   0.001635  0.175487 8.6073e-01    
## log(TA)                 0.000798   0.001999  0.399313 6.8973e-01    
## CtA                     0.013151   0.004001  3.287170 1.0406e-03 ** 
## EBITDAtA                0.009350   0.011996  0.779438 4.3587e-01    
## Leverage               -0.017764   0.007092 -2.504864 1.2379e-02 *  
## log(BM)                 0.003359   0.000680  4.941161 8.8392e-07 ***
## DivtoAsset             -0.072117   0.109183 -0.660515 5.0905e-01    
## l(log(MarCap), 1)      -0.004165   0.001865 -2.233140 2.5719e-02 *  
## ANews                  -0.001071   0.000798 -1.341361 1.8005e-01    
## NewsAverage            -0.002526   0.001591 -1.587685 1.1261e-01    
## log(NewsCount)         -0.002147   0.000564 -3.803775 1.4952e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.028976     Adj. R2: 0.266362
##                  Within R2: 0.055875
etable(RepIntVol_ols1, RepIntVol_ols2, RepIntVol_ols3,
       RepIntVol_ols1a, RepIntVol_ols2a, RepIntVol_ols3a,
       # vcov = "Ticker", 
       # headers = paste("(", 1:3, ")", sep = ""),
       tex = T)
## \begingroup
## \centering
## \begin{tabular}{lcccccc}
##    \tabularnewline \midrule \midrule
##    Dependent Variable: & \multicolumn{6}{c}{RepIntensity\_vol}\\
##    Model:                  & (1)             & (2)             & (3)             & (4)             & (5)                   & (6)\\  
##    \midrule
##    \emph{Variables}\\
##    AIA                     & -0.0052$^{***}$ & -0.0053$^{***}$ & -0.0039$^{***}$ &                 &                       &   \\   
##                            & (0.0005)        & (0.0005)        & (0.0005)        &                 &                       &   \\   
##    l(RepIntensity\_vol,1)  & 0.2047$^{***}$  & 0.2047$^{***}$  & 0.2026$^{***}$  & 0.2043$^{***}$  & 0.2044$^{***}$        & 0.2023$^{***}$\\   
##                            & (0.0351)        & (0.0372)        & (0.0374)        & (0.0351)        & (0.0372)              & (0.0374)\\   
##    log(Amihud\_monthly)    & -0.0020$^{***}$ & -0.0039$^{***}$ & -0.0045$^{***}$ & -0.0021$^{***}$ & -0.0040$^{***}$       & -0.0046$^{***}$\\   
##                            & (0.0005)        & (0.0007)        & (0.0007)        & (0.0005)        & (0.0007)              & (0.0007)\\   
##    OMRFlag                 & 0.0071$^{***}$  & 0.0071$^{***}$  & 0.0077$^{***}$  & 0.0071$^{***}$  & 0.0070$^{***}$        & 0.0077$^{***}$\\   
##                            & (0.0015)        & (0.0016)        & (0.0016)        & (0.0015)        & (0.0016)              & (0.0016)\\   
##    l(RET\_m1,1)            & -0.0104$^{***}$ & -0.0120$^{***}$ & -0.0121$^{***}$ & -0.0105$^{***}$ & -0.0120$^{***}$       & -0.0121$^{***}$\\   
##                            & (0.0018)        & (0.0019)        & (0.0020)        & (0.0018)        & (0.0019)              & (0.0020)\\   
##    l(RET\_m1,2)            & -0.0051$^{***}$ & -0.0032$^{*}$   & -0.0033$^{**}$  & -0.0053$^{***}$ & -0.0033$^{**}$        & -0.0033$^{**}$\\   
##                            & (0.0016)        & (0.0016)        & (0.0017)        & (0.0016)        & (0.0016)              & (0.0017)\\   
##    l(RET\_m1,3)            & -0.0017         & 0.0002          & 0.0004          & -0.0019         & $6.41\times 10^{-5}$  & 0.0003\\   
##                            & (0.0015)        & (0.0016)        & (0.0016)        & (0.0015)        & (0.0016)              & (0.0016)\\   
##    log(TA)                 &                 & 0.0006          & 0.0008          &                 & 0.0006                & 0.0008\\   
##                            &                 & (0.0020)        & (0.0020)        &                 & (0.0020)              & (0.0020)\\   
##    CtA                     &                 & 0.0143$^{***}$  & 0.0131$^{***}$  &                 & 0.0143$^{***}$        & 0.0132$^{***}$\\   
##                            &                 & (0.0041)        & (0.0040)        &                 & (0.0041)              & (0.0040)\\   
##    EBITDAtA                &                 & 0.0105          & 0.0094          &                 & 0.0105                & 0.0094\\   
##                            &                 & (0.0110)        & (0.0119)        &                 & (0.0111)              & (0.0120)\\   
##    Leverage                &                 & -0.0183$^{***}$ & -0.0182$^{**}$  &                 & -0.0178$^{**}$        & -0.0178$^{**}$\\   
##                            &                 & (0.0070)        & (0.0071)        &                 & (0.0070)              & (0.0071)\\   
##    log(BM)                 &                 & 0.0033$^{***}$  & 0.0033$^{***}$  &                 & 0.0033$^{***}$        & 0.0034$^{***}$\\   
##                            &                 & (0.0007)        & (0.0007)        &                 & (0.0007)              & (0.0007)\\   
##    DivtoAsset              &                 & -0.0694         & -0.0696         &                 & -0.0731               & -0.0721\\   
##                            &                 & (0.1040)        & (0.1088)        &                 & (0.1049)              & (0.1092)\\   
##    l(log(MarCap),1)        &                 & -0.0041$^{**}$  & -0.0042$^{**}$  &                 & -0.0040$^{**}$        & -0.0042$^{**}$\\   
##                            &                 & (0.0018)        & (0.0019)        &                 & (0.0018)              & (0.0019)\\   
##    ANews                   &                 &                 & -0.0011         &                 &                       & -0.0011\\   
##                            &                 &                 & (0.0008)        &                 &                       & (0.0008)\\   
##    NewsAverage             &                 &                 & -0.0024         &                 &                       & -0.0025\\   
##                            &                 &                 & (0.0016)        &                 &                       & (0.0016)\\   
##    log(NewsCount)          &                 &                 & -0.0022$^{***}$ &                 &                       & -0.0021$^{***}$\\   
##                            &                 &                 & (0.0006)        &                 &                       & (0.0006)\\   
##    AIAC                    &                 &                 &                 & -0.0076$^{***}$ & -0.0077$^{***}$       & -0.0057$^{***}$\\   
##                            &                 &                 &                 & (0.0008)        & (0.0008)              & (0.0008)\\   
##    \midrule
##    \emph{Fixed-effects}\\
##    Ticker                  & Yes             & Yes             & Yes             & Yes             & Yes                   & Yes\\  
##    time                    & Yes             & Yes             & Yes             & Yes             & Yes                   & Yes\\  
##    \midrule
##    \emph{Fit statistics}\\
##    Observations            & 41,730          & 39,836          & 39,470          & 41,730          & 39,836                & 39,470\\  
##    R$^2$                   & 0.28374         & 0.28965         & 0.29125         & 0.28388         & 0.28981               & 0.29138\\  
##    Within R$^2$            & 0.04901         & 0.05343         & 0.05570         & 0.04919         & 0.05365               & 0.05588\\  
##    \midrule \midrule
##    \multicolumn{7}{l}{\emph{Clustered (Ticker) standard-errors in parentheses}}\\
##    \multicolumn{7}{l}{\emph{Signif. Codes: ***: 0.01, **: 0.05, *: 0.1}}\\
## \end{tabular}
## \par\endgroup
if (0 ==1) {
  RepInt_ols_back <- feols(fml = RepIntensity ~ AIA + l(RepIntensity, -1) +
          Amihud_monthly + OMRFlag + # log(1 + NewsCount) +
          l(RET_m1, -1:0) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
          log(MarCap) + d(Volatility,1) + l(Volatility, -1) + log(TradeVol) + 
          ANews + NewsAverage + NewsCount
        | Ticker + time , # + Ticker^Year,
        data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
        cluster = c("Ticker"))
  
  pdShaRep3 <- panel(ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% 
                      filter(RepIntensity <= 0.10) %>% 
                      group_by(YM) %>% 
                      mutate(BM_med = median(BM, na.rm = T), 
                             Volatility_md = median(Volatility, na.rm = T)
                             ) %>% 
                      ungroup() %>% 
                      mutate(UnderPriced = BM > BM_med, 
                             HighVolatility = Volatility > Volatility_md
                             ), ~ Ticker + time)
  
  feols(fml = RepIntensity ~ 
          AIA + HighVolatility + AIA:HighVolatility + l(RepIntensity, 1) + 
          # AIA + UnderPriced + AIA:UnderPriced + l(RepIntensity, 1) + 
          # AIA + AIA:log(BM) + l(RepIntensity, 1) + 
          Amihud_monthly + OMRFlag + 
          l(RET_m1, 1:3) + log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
          l(log(MarCap), 1) + d(Volatility,1) + l(Volatility, 1) + log(TradeVol) + 
          ANews + NewsAverage + log(NewsCount)
        | Ticker + time, # + Ticker^yearqtr(YM), # + Ticker^Year,
        data = pdShaRep3, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
        cluster = c("Ticker")) %>%
    summary()
}

##### choose between good and bad firms 
feols(fml = RepIntensity ~ AIA*log(BM) + l(RepIntensity, 1) +
        ANews + NewsAverage + NewsCount + 
        Amihud_monthly + OMRFlag + # log(1 + NewsCount) +
        l(RET_m1, 1:3) + log(TA) + CtA + (EBITDAtA) + log(Leverage) + log(BM) + DivtoAsset + 
        l(log(MarCap), 1) + d(Volatility,1) + l(Volatility, 1) + log(TradeVol)
      | Ticker + time , # + Ticker^Year,
      data = pdShaRep, # %>% filter(RepIntensity_vol < 0.6), # %>% filter(missing3 == F), # %>% filter(RepIntensity > 34308*10^-10), 
      cluster = c("Ticker")) %>%
  summary()
## Warning in log(BM): NaNs produced
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                        Estimate  Std. Error   t value   Pr(>|t|)    
## AIA                -0.000952243 0.000139134 -6.844055 1.2124e-11 ***
## log(BM)             0.001207994 0.000148512  8.133968 1.0081e-15 ***
## l(RepIntensity, 1)  0.176546200 0.024521407  7.199677 1.0488e-12 ***
## ANews              -0.000528233 0.000163446 -3.231854 1.2626e-03 ** 
## NewsAverage         0.000196618 0.000370157  0.531175 5.9539e-01    
## NewsCount          -0.000000191 0.000000356 -0.535340 5.9251e-01    
## Amihud_monthly      0.011245068 0.009039153  1.244040 2.1372e-01    
## OMRFlag             0.001620989 0.000296177  5.473038 5.3583e-08 ***
## l(RET_m1, 1)       -0.002570903 0.000455517 -5.643919 2.0624e-08 ***
## l(RET_m1, 2)       -0.001276676 0.000391708 -3.259259 1.1476e-03 ** 
## l(RET_m1, 3)       -0.000551883 0.000367485 -1.501787 1.3341e-01    
## log(TA)            -0.002143216 0.000351934 -6.089817 1.5095e-09 ***
## CtA                 0.002077677 0.000783683  2.651171 8.1245e-03 ** 
## EBITDAtA            0.007164967 0.003061652  2.340229 1.9431e-02 *  
## log(Leverage)       0.001249335 0.000306828  4.071771 4.9643e-05 ***
## DivtoAsset         -0.019308889 0.020258124 -0.953143 3.4071e-01    
## l(log(MarCap), 1)   0.001603031 0.000313150  5.119048 3.5615e-07 ***
## d(Volatility, 1)   -0.043143699 0.007357268 -5.864092 5.7985e-09 ***
## l(Volatility, 1)   -0.041742714 0.008921180 -4.679058 3.2014e-06 ***
## log(TradeVol)       0.001964307 0.000168222 11.676885  < 2.2e-16 ***
## AIA:log(BM)        -0.000304146 0.000073882 -4.116639 4.1011e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005404     Adj. R2: 0.231338
##                  Within R2: 0.057682
## 4. IV regression 2sls* ------ 
pdShaRep <- panel(ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% 
                    mutate(lambda = TradeVol / ShaOut) %>% 
                    # mutate(Amihud_monthly = log(Amihud_monthly)) %>% 
                    # filter(OMRFlag == 0) %>% 
                    filter(RepIntensity <= 0.10) , ~ Ticker + time)

fe_2sls <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
                   # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                   # MarCap + Month + Volatility + TradeVol
                   l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + # log(ProgramMonth) + 
                   l(log(MarCap), 1) # + ShortInterest + d(ShortInterest,1) # + d(Volatility,1) + l(Volatility, 1) + TradeVol_scaled # + lambda
                 | Ticker + time | AIA ~ MarketAIA, # + Ticker^yearqtr(YM) # + Ticker^YQ # + sic*time
                 data = pdShaRep, # [pdShaRep$AIA < 4.0,], # [pdShaRep$RepIntensity > 0,], 
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
summary(fe_2sls, stage = 1:2)
## IV: First stage: AIA
## TSLS estimation, Dep. Var.: AIA, Endo.: AIA, Instr.: MarketAIA
## First stage: Dep. Var.: AIA
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error     t value   Pr(>|t|)    
## MarketAIA           -1246.246377   5.213920 -239.022901  < 2.2e-16 ***
## l(RepIntensity, 1)     -0.038911   0.108752   -0.357791 7.2056e-01    
## ANews                   0.012178   0.004044    3.011646 2.6515e-03 ** 
## NewsAverage            -0.021503   0.008629   -2.492072 1.2831e-02 *  
## log(NewsCount)          0.017287   0.002222    7.780849 1.5196e-14 ***
## log(Amihud_monthly)    -0.006228   0.003398   -1.832821 6.7071e-02 .  
## OMRFlag                -0.005216   0.003510   -1.486078 1.3752e-01    
## l(RET_m1, 1)           -0.014092   0.008494   -1.659027 9.7366e-02 .  
## l(RET_m1, 2)           -0.005770   0.008700   -0.663160 5.0735e-01    
## l(RET_m1, 3)            0.002708   0.011858    0.228379 8.1939e-01    
## log(TA)                 0.002704   0.011175    0.241974 8.0884e-01    
## CtA                    -0.020015   0.017653   -1.133812 2.5709e-01    
## EBITDAtA                0.045051   0.040707    1.106719 2.6863e-01    
## Leverage               -0.028830   0.041254   -0.698833 4.8479e-01    
## log(BM)                -0.000962   0.002774   -0.347000 7.2865e-01    
## DivtoAsset             -0.856941   0.631948   -1.356031 1.7534e-01    
## l(log(MarCap), 1)      -0.005619   0.008903   -0.631094 5.2810e-01    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.146318     Adj. R2: 0.954451
##                  Within R2: 0.866112
## F-test (1st stage): stat = 211,915.5, p < 2.2e-16, on 1 and 39,351 DoF.
## 
## IV: Second stage
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA             -0.000564   0.000110  -5.132138 3.3273e-07 ***
## l(RepIntensity, 1)   0.175804   0.024377   7.211989 9.6171e-13 ***
## ANews               -0.000525   0.000155  -3.379464 7.4907e-04 ***
## NewsAverage          0.000131   0.000347   0.377680 7.0573e-01    
## log(NewsCount)       0.000111   0.000102   1.087722 2.7693e-01    
## log(Amihud_monthly) -0.002069   0.000150 -13.818555  < 2.2e-16 ***
## OMRFlag              0.001651   0.000297   5.562898 3.2538e-08 ***
## l(RET_m1, 1)        -0.004001   0.000478  -8.369848  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001564   0.000396  -3.944144 8.4615e-05 ***
## l(RET_m1, 3)        -0.000573   0.000373  -1.535225 1.2499e-01    
## log(TA)             -0.000848   0.000421  -2.015178 4.4104e-02 *  
## CtA                  0.001771   0.000764   2.319118 2.0552e-02 *  
## EBITDAtA             0.005004   0.002832   1.766994 7.7478e-02 .  
## Leverage             0.000123   0.001460   0.084518 9.3266e-01    
## log(BM)              0.000945   0.000139   6.816235 1.4614e-11 ***
## DivtoAsset          -0.009282   0.017855  -0.519857 6.0326e-01    
## l(log(MarCap), 1)   -0.001178   0.000386  -3.049153 2.3440e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230749
##                  Within R2: 0.056862
## F-test (1st stage), AIA: stat = 211,915.5    , p < 2.2e-16 , on 1 and 39,351 DoF.
##              Wu-Hausman: stat =       2.08848, p = 0.148421, on 1 and 38,122 DoF.
  ## %% NOTE: the results is robustness when adding industry-year-month interactions and even firm-year-quarter interactions, although the magnitude is halved for the latter case and the significance level drops to 5% level. [May 4, 2024]
## other alternative controls: 
  feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
          # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
          ANews + NewsAverage + log(NewsCount) + 
          log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
          # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
          # MarCap + Month + Volatility + TradeVol
          l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + log(ProgramMonth) + 
          l(log(MarCap), 1) + ShortInterest + d(ShortInterest,1) # + d(Volatility,1) + l(Volatility, 1) + TradeVol_scaled # + lambda
        | Ticker + time | AIA ~ MarketAIA, # + Ticker^yearqtr(YM) # + Ticker^YQ # + sic*time
        data = pdShaRep, # [pdShaRep$AIA < 4.0,], # [pdShaRep$RepIntensity > 0,], 
        cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,679 observations removed because of NA and infinite values (RHS: 34,679).
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,106 
## Fixed-effects: Ticker: 1,216,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA             -0.000542   0.000109  -4.983317 7.1548e-07 ***
## l(RepIntensity, 1)   0.169328   0.024563   6.893594 8.7206e-12 ***
## ANews               -0.000568   0.000155  -3.660698 2.6233e-04 ***
## NewsAverage          0.000241   0.000342   0.703250 4.8203e-01    
## log(NewsCount)       0.000108   0.000102   1.060362 2.8919e-01    
## log(Amihud_monthly) -0.002079   0.000152 -13.713430  < 2.2e-16 ***
## OMRFlag              0.000445   0.000337   1.321368 1.8663e-01    
## l(RET_m1, 1)        -0.003827   0.000483  -7.925154 5.1211e-15 ***
## l(RET_m1, 2)        -0.001392   0.000408  -3.416038 6.5638e-04 ***
## l(RET_m1, 3)        -0.000525   0.000372  -1.410464 1.5866e-01    
## log(TA)             -0.000833   0.000434  -1.920582 5.5018e-02 .  
## CtA                  0.002030   0.000774   2.621826 8.8553e-03 ** 
## EBITDAtA             0.004657   0.002830   1.645181 1.0019e-01    
## Leverage             0.000337   0.001479   0.228011 8.1968e-01    
## log(BM)              0.000932   0.000139   6.703427 3.1094e-11 ***
## DivtoAsset          -0.010046   0.017029  -0.589949 5.5533e-01    
## log(ProgramMonth)   -0.000497   0.000064  -7.762568 1.7572e-14 ***
## l(log(MarCap), 1)   -0.001285   0.000390  -3.290339 1.0294e-03 ** 
## ShortInterest       -0.000960   0.001053  -0.911698 3.6211e-01    
## d(ShortInterest, 1)  0.017937   0.006102   2.939345 3.3512e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005403     Adj. R2: 0.234962
##                  Within R2: 0.062287
## F-test (1st stage), AIA: stat = 208,231.9    , p < 2.2e-16, on 1 and 38,984 DoF.
##              Wu-Hausman: stat =       2.12353, p = 0.14506, on 1 and 37,768 DoF.
  feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
          # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
          ANews + NewsAverage + log(NewsCount) + 
          log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
          # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
          # MarCap + Month + Volatility + TradeVol
          l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + log(ProgramMonth) + 
          l(log(MarCap), 1) + ShortInterest + d(ShortInterest,1) # + d(Volatility,1) + l(Volatility, 1) + TradeVol_scaled # + lambda
        | Ticker + time + sic*time | AIA ~ MarketAIA, # + Ticker^yearqtr(YM) # + Ticker^YQ # 
        data = pdShaRep, # [pdShaRep$AIA < 4.0,], # [pdShaRep$RepIntensity > 0,], 
        cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,679 observations removed because of NA and infinite values (RHS: 34,679, Fixed-effects: 1,243).
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,106 
## Fixed-effects: Ticker: 1,216,  time: 102,  sic: 293,  time:sic: 17,417
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error   t value   Pr(>|t|)    
## fit_AIA             -0.000614   0.000150 -4.095284 4.4955e-05 ***
## l(RepIntensity, 1)   0.155455   0.035916  4.328342 1.6259e-05 ***
## ANews               -0.000375   0.000237 -1.579275 1.1453e-01    
## NewsAverage          0.000333   0.000504  0.661757 5.0825e-01    
## log(NewsCount)       0.000089   0.000164  0.539580 5.8959e-01    
## log(Amihud_monthly) -0.002309   0.000237 -9.738466  < 2.2e-16 ***
## OMRFlag              0.000238   0.000507  0.470075 6.3839e-01    
## l(RET_m1, 1)        -0.003848   0.000802 -4.795919 1.8198e-06 ***
## l(RET_m1, 2)        -0.001418   0.000668 -2.122507 3.3997e-02 *  
## l(RET_m1, 3)         0.000063   0.000692  0.091122 9.2741e-01    
## log(TA)              0.000122   0.000723  0.169169 8.6569e-01    
## CtA                  0.001969   0.001103  1.784903 7.4526e-02 .  
## EBITDAtA             0.000288   0.003410  0.084314 9.3282e-01    
## Leverage            -0.002031   0.002288 -0.887708 3.7487e-01    
## log(BM)              0.000388   0.000265  1.466472 1.4278e-01    
## DivtoAsset          -0.085269   0.113446 -0.751620 4.5243e-01    
## log(ProgramMonth)   -0.000434   0.000100 -4.351621 1.4648e-05 ***
## l(log(MarCap), 1)   -0.002703   0.000656 -4.120572 4.0355e-05 ***
## ShortInterest       -0.002359   0.001707 -1.381835 1.6728e-01    
## d(ShortInterest, 1)  0.023761   0.007153  3.321878 9.2073e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.00398     Adj. R2: 0.218354
##                 Within R2: 0.052638
## F-test (1st stage), AIA: stat = 81,168.0    , p < 2.2e-16 , on 1 and 21,276 DoF.
##              Wu-Hausman: stat =      2.21596, p = 0.136605, on 1 and 20,060 DoF.
  feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
          # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
          ANews + NewsAverage + log(NewsCount) + 
          log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
          # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
          # MarCap + Month + Volatility + TradeVol
          l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + log(ProgramMonth) + 
          l(log(MarCap), 1) + ShortInterest + d(ShortInterest,1) # + d(Volatility,1) + l(Volatility, 1) + TradeVol_scaled # + lambda
        | Ticker + time + Ticker^yearqtr(YM) | AIA ~ MarketAIA, #  # + Ticker^YQ # 
        data = pdShaRep, # [pdShaRep$AIA < 4.0,], # [pdShaRep$RepIntensity > 0,], 
        cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,679 observations removed because of NA and infinite values (RHS: 34,679).
## The exogenous variable 'DivtoAsset' have been removed because of collinearity (see $collin.var).
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,106 
## Fixed-effects: Ticker: 1,216,  time: 102,  Ticker^yearqtr(YM): 14,330
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA             -0.000360   0.000127  -2.837651 4.6202e-03 ** 
## l(RepIntensity, 1)  -0.241473   0.016391 -14.731862  < 2.2e-16 ***
## ANews               -0.000419   0.000174  -2.406750 1.6244e-02 *  
## NewsAverage         -0.000206   0.000389  -0.530672 5.9574e-01    
## log(NewsCount)       0.000037   0.000121   0.308599 7.5768e-01    
## log(Amihud_monthly) -0.002349   0.000222 -10.568056  < 2.2e-16 ***
## OMRFlag             -0.001194   0.000526  -2.267388 2.3542e-02 *  
## l(RET_m1, 1)        -0.002655   0.000640  -4.147908 3.5886e-05 ***
## l(RET_m1, 2)        -0.002952   0.000790  -3.736964 1.9491e-04 ***
## l(RET_m1, 3)        -0.001628   0.000594  -2.738064 6.2705e-03 ** 
## log(TA)              0.001418   0.002678   0.529464 5.9658e-01    
## CtA                  0.016514   0.003690   4.475100 8.3540e-06 ***
## EBITDAtA            -0.021848   0.005800  -3.766794 1.7328e-04 ***
## Leverage            -0.010991   0.007630  -1.440608 1.4995e-01    
## log(BM)              0.007076   0.001360   5.203745 2.2909e-07 ***
## log(ProgramMonth)   -0.000731   0.000204  -3.584367 3.5129e-04 ***
## l(log(MarCap), 1)    0.001087   0.000997   1.090759 2.7560e-01    
## ShortInterest        0.000884   0.007167   0.123275 9.0191e-01    
## d(ShortInterest, 1)  0.010209   0.008675   1.176770 2.3952e-01    
## ... 1 variable was removed because of collinearity (DivtoAsset)
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.003972     Adj. R2: 0.333894
##                  Within R2: 0.077322
## F-test (1st stage), AIA: stat = 200,845.5, p < 2.2e-16, on 1 and 38,985 DoF.
##              Wu-Hausman: stat =      NA  , p = NA     , on 1 and 23,440 DoF.
    feols(fml = RepIntensity ~ AIA + MarketAIA + l(RepIntensity, 1) + 
            # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
            ANews + NewsAverage + log(NewsCount) + 
            log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
            # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
            # MarCap + Month + Volatility + TradeVol
            l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
            l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + log(TradeVol) # + lambda
          | Ticker + time , # Ticker^yearqtr(YM)
          data = pdShaRep, # [pdShaRep$AIA < 4.0,], # [pdShaRep$RepIntensity > 0,], 
          cluster = c("Ticker")) 
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## AIA                 -0.000267   0.000142  -1.871037 6.1578e-02 .  
## MarketAIA            0.371119   0.202356   1.833989 6.6897e-02 .  
## l(RepIntensity, 1)   0.175816   0.024375   7.213094 9.5426e-13 ***
## ANews               -0.000529   0.000155  -3.400685 6.9377e-04 ***
## NewsAverage          0.000137   0.000347   0.395878 6.9226e-01    
## log(NewsCount)       0.000106   0.000102   1.040029 2.9853e-01    
## log(Amihud_monthly) -0.002067   0.000150 -13.806484  < 2.2e-16 ***
## OMRFlag              0.001652   0.000297   5.570175 3.1240e-08 ***
## ... 10 coefficients remaining (display them with summary() or use argument n)
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230779
##                  Within R2: 0.056923
fe_2sls_nocontrol <- feols(fml = RepIntensity ~ l(RepIntensity, 1)
                 | Ticker + time  + Ticker^yearqtr(YM)| AIA ~ MarketAIA , # + Ticker^Year 
                 data = pdShaRep, 
                 cluster = c("Ticker"))
## NOTE: 12,149 observations removed because of NA values (RHS: 12,149).
fe_2slsC <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + OMRFlag + 
                   l(RET_m1, 1:3)+ log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                   l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + log(TradeVol)
                 | Ticker + time | AIAC ~ MarketAIAC , #  + Ticker^yearqtr(YM) 
                 data = pdShaRep, 
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
fe_2slsC_nocontrol <- feols(fml = RepIntensity ~ 1
                  | Ticker + time | AIAC ~ MarketAIAC , # + Ticker^Year 
                  data = pdShaRep, 
                  cluster = c("Ticker"))

fe_2sls_vol <- feols(fml = RepIntensity_vol ~ l(RepIntensity_vol, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
                   # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                   # MarCap + Month + Volatility + TradeVol
                   l(RET_m1, 1:3)+ log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                   l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + log(TradeVol)
                 | Ticker + time | AIA ~ MarketAIA , # + Ticker^Year 
                 data = pdShaRep, 
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
fe_2slsC_vol <- feols(fml = RepIntensity_vol ~ l(RepIntensity_vol, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
                   # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                   # MarCap + Month + Volatility + TradeVol
                   l(RET_m1, 1:3)+ log(TA) + CtA + EBITDAtA + (Leverage) + log(BM) + DivtoAsset + 
                   l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + log(TradeVol)
                 | Ticker + time | AIAC ~ MarketAIAC , # + Ticker^Year 
                 data = pdShaRep, 
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
fe_2sls
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA             -0.000564   0.000110  -5.132138 3.3273e-07 ***
## l(RepIntensity, 1)   0.175804   0.024377   7.211989 9.6171e-13 ***
## ANews               -0.000525   0.000155  -3.379464 7.4907e-04 ***
## NewsAverage          0.000131   0.000347   0.377680 7.0573e-01    
## log(NewsCount)       0.000111   0.000102   1.087722 2.7693e-01    
## log(Amihud_monthly) -0.002069   0.000150 -13.818555  < 2.2e-16 ***
## OMRFlag              0.001651   0.000297   5.562898 3.2538e-08 ***
## l(RET_m1, 1)        -0.004001   0.000478  -8.369848  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001564   0.000396  -3.944144 8.4615e-05 ***
## l(RET_m1, 3)        -0.000573   0.000373  -1.535225 1.2499e-01    
## log(TA)             -0.000848   0.000421  -2.015178 4.4104e-02 *  
## CtA                  0.001771   0.000764   2.319118 2.0552e-02 *  
## EBITDAtA             0.005004   0.002832   1.766994 7.7478e-02 .  
## Leverage             0.000123   0.001460   0.084518 9.3266e-01    
## log(BM)              0.000945   0.000139   6.816235 1.4614e-11 ***
## DivtoAsset          -0.009282   0.017855  -0.519857 6.0326e-01    
## l(log(MarCap), 1)   -0.001178   0.000386  -3.049153 2.3440e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230749
##                  Within R2: 0.056862
## F-test (1st stage), AIA: stat = 211,915.5    , p < 2.2e-16 , on 1 and 39,351 DoF.
##              Wu-Hausman: stat =       2.08848, p = 0.148421, on 1 and 38,122 DoF.
fe_2slsC
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIAC, Instr.: MarketAIAC
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIAC            -0.000770   0.000158  -4.890097 1.1414e-06 ***
## l(RepIntensity, 1)   0.175744   0.024373   7.210665 9.7073e-13 ***
## ANews               -0.000524   0.000155  -3.367864 7.8100e-04 ***
## NewsAverage          0.000092   0.000347   0.265294 7.9083e-01    
## log(NewsCount)       0.000114   0.000103   1.102129 2.7062e-01    
## log(Amihud_monthly) -0.002080   0.000150 -13.868930  < 2.2e-16 ***
## OMRFlag              0.001647   0.000297   5.546434 3.5672e-08 ***
## l(RET_m1, 1)        -0.003999   0.000478  -8.361985  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001575   0.000397  -3.969515 7.6195e-05 ***
## l(RET_m1, 3)        -0.000586   0.000373  -1.571459 1.1633e-01    
## log(TA)             -0.000846   0.000421  -2.009772 4.4674e-02 *  
## CtA                  0.001768   0.000764   2.314926 2.0781e-02 *  
## EBITDAtA             0.005010   0.002840   1.764187 7.7949e-02 .  
## Leverage             0.000165   0.001459   0.113279 9.0983e-01    
## log(BM)              0.000946   0.000139   6.826498 1.3642e-11 ***
## DivtoAsset          -0.009600   0.017967  -0.534305 5.9323e-01    
## l(log(MarCap), 1)   -0.001171   0.000386  -3.033077 2.4715e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230792
##                  Within R2: 0.056915
## F-test (1st stage), AIAC: stat = 329,073.2     , p < 2.2e-16 , on 1 and 39,351 DoF.
##               Wu-Hausman: stat =       0.413423, p = 0.520241, on 1 and 38,122 DoF.
fe_2sls_vol
## TSLS estimation, Dep. Var.: RepIntensity_vol, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity_vol
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error   t value   Pr(>|t|)    
## fit_AIA                -0.004347   0.000595 -7.304378 4.9968e-13 ***
## l(RepIntensity_vol, 1)  0.202606   0.037375  5.420835 7.1355e-08 ***
## ANews                  -0.001068   0.000795 -1.343191 1.7946e-01    
## NewsAverage            -0.002160   0.001564 -1.381224 1.6746e-01    
## log(NewsCount)         -0.002138   0.000565 -3.784395 1.6151e-04 ***
## log(Amihud_monthly)    -0.004551   0.000740 -6.152837 1.0283e-09 ***
## OMRFlag                 0.007728   0.001614  4.789168 1.8786e-06 ***
## l(RET_m1, 1)           -0.012152   0.001968 -6.174210 9.0207e-10 ***
## l(RET_m1, 2)           -0.003264   0.001656 -1.971727 4.8865e-02 *  
## l(RET_m1, 3)            0.000378   0.001634  0.231424 8.1702e-01    
## log(TA)                 0.000785   0.002000  0.392559 6.9471e-01    
## CtA                     0.013197   0.004004  3.296313 1.0076e-03 ** 
## EBITDAtA                0.009254   0.011940  0.775080 4.3844e-01    
## Leverage               -0.018019   0.007099 -2.538285 1.1262e-02 *  
## log(BM)                 0.003348   0.000680  4.924339 9.6184e-07 ***
## DivtoAsset             -0.069913   0.108680 -0.643293 5.2015e-01    
## l(log(MarCap), 1)      -0.004200   0.001865 -2.251636 2.4521e-02 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.028979     Adj. R2: 0.266196
##                  Within R2: 0.055661
## F-test (1st stage), AIA: stat = 211,905.7    , p < 2.2e-16 , on 1 and 39,351 DoF.
##              Wu-Hausman: stat =       7.56539, p = 0.005953, on 1 and 38,122 DoF.
fe_2slsC_vol
## TSLS estimation, Dep. Var.: RepIntensity_vol, Endo.: AIAC, Instr.: MarketAIAC
## Second stage: Dep. Var.: RepIntensity_vol
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error   t value   Pr(>|t|)    
## fit_AIAC               -0.006000   0.000831 -7.223320 8.8786e-13 ***
## l(RepIntensity_vol, 1)  0.202334   0.037366  5.414892 7.3709e-08 ***
## ANews                  -0.001053   0.000798 -1.318687 1.8752e-01    
## NewsAverage            -0.002441   0.001583 -1.542058 1.2332e-01    
## log(NewsCount)         -0.002117   0.000565 -3.745145 1.8864e-04 ***
## log(Amihud_monthly)    -0.004639   0.000739 -6.274595 4.8497e-10 ***
## OMRFlag                 0.007704   0.001615  4.770377 2.0592e-06 ***
## l(RET_m1, 1)           -0.012137   0.001969 -6.162764 9.6767e-10 ***
## l(RET_m1, 2)           -0.003353   0.001657 -2.023628 4.3225e-02 *  
## l(RET_m1, 3)            0.000271   0.001635  0.165908 8.6826e-01    
## log(TA)                 0.000803   0.001998  0.401899 6.8783e-01    
## CtA                     0.013180   0.004005  3.290899 1.0271e-03 ** 
## EBITDAtA                0.009292   0.012010  0.773752 4.3923e-01    
## Leverage               -0.017683   0.007094 -2.492790 1.2805e-02 *  
## log(BM)                 0.003362   0.000679  4.950421 8.4367e-07 ***
## DivtoAsset             -0.072413   0.109153 -0.663409 5.0719e-01    
## l(log(MarCap), 1)      -0.004141   0.001864 -2.221834 2.6476e-02 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.028976     Adj. R2: 0.266357
##                  Within R2: 0.055868
## F-test (1st stage), AIAC: stat = 329,083.2    , p < 2.2e-16 , on 1 and 39,351 DoF.
##               Wu-Hausman: stat =       2.46053, p = 0.116747, on 1 and 38,122 DoF.
fitstat(fe_2sls, ~ cd + r2 + AIC + BIC + ivfall + ivwaldall + wh, cluster = 'Ticker')
## Warning in log(BM): NaNs produced

## Warning in log(BM): NaNs produced
##     Cragg-Donald: 212,540.2
##               R2: 0.256983
##              AIC: -297,375.2
##              BIC: -285,813.5
## F-test (IV only): stat = 49.4    , p = 2.075e-12, on 1 and 39,351 DoF.
##   Wald (IV only): stat = 26.3    , p = 2.878e-7 , on 1 and 39,351 DoF, VCOV: Clustered (Ticker).
##       Wu-Hausman: stat =  2.08848, p = 0.148421 , on 1 and 38,122 DoF.
fitstat(fe_2sls_vol, ~ r2 + ivfall + ivwaldall + wh, cluster = 'Ticker')
##               R2: 0.29122
## F-test (IV only): stat = 102.1    , p < 2.2e-16  , on 1 and 39,351 DoF.
##   Wald (IV only): stat =  53.4    , p = 2.838e-13, on 1 and 39,351 DoF, VCOV: Clustered (Ticker).
##       Wu-Hausman: stat =   7.56539, p = 0.005953 , on 1 and 38,122 DoF.
if (0==1) {
  fe_2sls <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
                     # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                     ANews + NewsAverage + log(NewsCount) + 
                     Amihud_monthly + OMRFlag + # log(1 + NewsCount) +
                     # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                     # MarCap + Month + Volatility + TradeVol
                     l(RET_m1, 1:3)+ log(TA) + CtA + EBITDAtA + log(Leverage) + (BM) + DivtoAsset + 
                     l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1)#  + log(TradeVol)
                   | Ticker + time | AIA ~ MarketAIA , # + Ticker^Year 
                   data = pdShaRep, 
                   cluster = c("Ticker"))
  fitstat(fe_2sls, ~ r2 + AIC + BIC + ivfall + ivwaldall + wh, cluster = 'Ticker')
}

summary(fe_2sls, stage = 1)
## TSLS estimation, Dep. Var.: AIA, Endo.: AIA, Instr.: MarketAIA
## First stage: Dep. Var.: AIA
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error     t value   Pr(>|t|)    
## MarketAIA           -1246.246377   5.213920 -239.022901  < 2.2e-16 ***
## l(RepIntensity, 1)     -0.038911   0.108752   -0.357791 7.2056e-01    
## ANews                   0.012178   0.004044    3.011646 2.6515e-03 ** 
## NewsAverage            -0.021503   0.008629   -2.492072 1.2831e-02 *  
## log(NewsCount)          0.017287   0.002222    7.780849 1.5196e-14 ***
## log(Amihud_monthly)    -0.006228   0.003398   -1.832821 6.7071e-02 .  
## OMRFlag                -0.005216   0.003510   -1.486078 1.3752e-01    
## l(RET_m1, 1)           -0.014092   0.008494   -1.659027 9.7366e-02 .  
## l(RET_m1, 2)           -0.005770   0.008700   -0.663160 5.0735e-01    
## l(RET_m1, 3)            0.002708   0.011858    0.228379 8.1939e-01    
## log(TA)                 0.002704   0.011175    0.241974 8.0884e-01    
## CtA                    -0.020015   0.017653   -1.133812 2.5709e-01    
## EBITDAtA                0.045051   0.040707    1.106719 2.6863e-01    
## Leverage               -0.028830   0.041254   -0.698833 4.8479e-01    
## log(BM)                -0.000962   0.002774   -0.347000 7.2865e-01    
## DivtoAsset             -0.856941   0.631948   -1.356031 1.7534e-01    
## l(log(MarCap), 1)      -0.005619   0.008903   -0.631094 5.2810e-01    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.146318     Adj. R2: 0.954451
##                  Within R2: 0.866112
## F-test (1st stage): stat = 211,915.5, p < 2.2e-16, on 1 and 39,351 DoF.
summary(fe_2sls, stage = 2)
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA             -0.000564   0.000110  -5.132138 3.3273e-07 ***
## l(RepIntensity, 1)   0.175804   0.024377   7.211989 9.6171e-13 ***
## ANews               -0.000525   0.000155  -3.379464 7.4907e-04 ***
## NewsAverage          0.000131   0.000347   0.377680 7.0573e-01    
## log(NewsCount)       0.000111   0.000102   1.087722 2.7693e-01    
## log(Amihud_monthly) -0.002069   0.000150 -13.818555  < 2.2e-16 ***
## OMRFlag              0.001651   0.000297   5.562898 3.2538e-08 ***
## l(RET_m1, 1)        -0.004001   0.000478  -8.369848  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001564   0.000396  -3.944144 8.4615e-05 ***
## l(RET_m1, 3)        -0.000573   0.000373  -1.535225 1.2499e-01    
## log(TA)             -0.000848   0.000421  -2.015178 4.4104e-02 *  
## CtA                  0.001771   0.000764   2.319118 2.0552e-02 *  
## EBITDAtA             0.005004   0.002832   1.766994 7.7478e-02 .  
## Leverage             0.000123   0.001460   0.084518 9.3266e-01    
## log(BM)              0.000945   0.000139   6.816235 1.4614e-11 ***
## DivtoAsset          -0.009282   0.017855  -0.519857 6.0326e-01    
## l(log(MarCap), 1)   -0.001178   0.000386  -3.049153 2.3440e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230749
##                  Within R2: 0.056862
## F-test (1st stage), AIA: stat = 211,915.5    , p < 2.2e-16 , on 1 and 39,351 DoF.
##              Wu-Hausman: stat =       2.08848, p = 0.148421, on 1 and 38,122 DoF.
etable(summary(fe_2sls, stage = 1),
       summary(fe_2sls_vol, stage = 1),
       summary(fe_2slsC, stage = 1),
       summary(fe_2slsC_vol, stage = 1),
       fitstat = ~ . + ivf1 + ivwaldall + wh + wh.p, 
       tex = T)
## \begingroup
## \centering
## \begin{tabular}{lcccc}
##    \tabularnewline \midrule \midrule
##    Dependent Variables: & \multicolumn{2}{c}{AIA} & \multicolumn{2}{c}{AIAC}\\
##    Model:                  & (1)              & (2)              & (3)              & (4)\\  
##    \midrule
##    \emph{Variables}\\
##    MarketAIA               & -1,246.2$^{***}$ & -1,246.3$^{***}$ &                  &   \\   
##                            & (5.214)          & (5.214)          &                  &   \\   
##    l(RepIntensity,1)       & -0.0389          &                  & -0.0376          &   \\   
##                            & (0.1088)         &                  & (0.0784)         &   \\   
##    ANews                   & 0.0122$^{***}$   & 0.0122$^{***}$   & 0.0082$^{***}$   & 0.0082$^{***}$\\   
##                            & (0.0040)         & (0.0040)         & (0.0025)         & (0.0025)\\   
##    NewsAverage             & -0.0215$^{**}$   & -0.0215$^{**}$   & -0.0143$^{**}$   & -0.0142$^{**}$\\   
##                            & (0.0086)         & (0.0086)         & (0.0055)         & (0.0055)\\   
##    log(NewsCount)          & 0.0173$^{***}$   & 0.0173$^{***}$   & 0.0123$^{***}$   & 0.0123$^{***}$\\   
##                            & (0.0022)         & (0.0022)         & (0.0015)         & (0.0015)\\   
##    log(Amihud\_monthly)    & -0.0062$^{*}$    & -0.0062$^{*}$    & -0.0077$^{***}$  & -0.0077$^{***}$\\   
##                            & (0.0034)         & (0.0034)         & (0.0022)         & (0.0022)\\   
##    OMRFlag                 & -0.0052          & -0.0052          & -0.0045$^{*}$    & -0.0045$^{*}$\\   
##                            & (0.0035)         & (0.0035)         & (0.0025)         & (0.0025)\\   
##    l(RET\_m1,1)            & -0.0141$^{*}$    & -0.0140$^{*}$    & -0.0103$^{**}$   & -0.0103$^{**}$\\   
##                            & (0.0085)         & (0.0085)         & (0.0051)         & (0.0051)\\   
##    l(RET\_m1,2)            & -0.0058          & -0.0057          & -0.0056          & -0.0055\\   
##                            & (0.0087)         & (0.0087)         & (0.0056)         & (0.0056)\\   
##    l(RET\_m1,3)            & 0.0027           & 0.0027           & -0.0013          & -0.0013\\   
##                            & (0.0119)         & (0.0118)         & (0.0062)         & (0.0062)\\   
##    log(TA)                 & 0.0027           & 0.0027           & 0.0043           & 0.0043\\   
##                            & (0.0112)         & (0.0112)         & (0.0077)         & (0.0077)\\   
##    CtA                     & -0.0200          & -0.0200          & -0.0168          & -0.0168\\   
##                            & (0.0176)         & (0.0177)         & (0.0134)         & (0.0134)\\   
##    EBITDAtA                & 0.0450           & 0.0449           & 0.0352           & 0.0351\\   
##                            & (0.0407)         & (0.0407)         & (0.0312)         & (0.0311)\\   
##    Leverage                & -0.0288          & -0.0289          & -0.0198          & -0.0199\\   
##                            & (0.0413)         & (0.0413)         & (0.0272)         & (0.0272)\\   
##    log(BM)                 & -0.0010          & -0.0010          & -0.0011          & -0.0011\\   
##                            & (0.0028)         & (0.0028)         & (0.0022)         & (0.0022)\\   
##    DivtoAsset              & -0.8569          & -0.8568          & -0.5032          & -0.5030\\   
##                            & (0.6319)         & (0.6316)         & (0.4763)         & (0.4759)\\   
##    l(log(MarCap),1)        & -0.0056          & -0.0056          & -0.0053          & -0.0053\\   
##                            & (0.0089)         & (0.0089)         & (0.0061)         & (0.0061)\\   
##    l(RepIntensity\_vol,1)  &                  & -0.0094          &                  & -0.0093\\   
##                            &                  & (0.0224)         &                  & (0.0166)\\   
##    MarketAIAC              &                  &                  & -1,234.8$^{***}$ & -1,234.9$^{***}$\\   
##                            &                  &                  & (6.101)          & (6.100)\\   
##    \midrule
##    \emph{Fixed-effects}\\
##    Ticker                  & Yes              & Yes              & Yes              & Yes\\  
##    time                    & Yes              & Yes              & Yes              & Yes\\  
##    \midrule
##    \emph{Fit statistics}\\
##    Observations            & 39,470           & 39,470           & 39,470           & 39,470\\  
##    R$^2$                   & 0.95600          & 0.95600          & 0.97451          & 0.97451\\  
##    Within R$^2$            & 0.86611          & 0.86611          & 0.90870          & 0.90870\\  
##    F-test (1st stage)      & 211,915.5        & 211,905.7        & 329,073.2        & 329,083.2\\  
##    Wald (IV only)          & 57,131.9         & 57,131.8         & 40,972.5         & 40,976.0\\  
##    \midrule \midrule
##    \multicolumn{5}{l}{\emph{Clustered (Ticker) standard-errors in parentheses}}\\
##    \multicolumn{5}{l}{\emph{Signif. Codes: ***: 0.01, **: 0.05, *: 0.1}}\\
## \end{tabular}
## \par\endgroup
etable(summary(fe_2sls, stage = 2),
       summary(fe_2sls_vol, stage = 2),
       summary(fe_2slsC, stage = 2),
       summary(fe_2slsC_vol, stage = 2),
       fitstat = ~ . + ivfall + ivwaldall + wh + wh.p, 
       tex = F)
##                       summary(fe_2sls, .. summary(fe_2sls_v..
## Dependent Var.:              RepIntensity    RepIntensity_vol
##                                                              
## AIA                   -0.0006*** (0.0001) -0.0043*** (0.0006)
## l(RepIntensity,1)      0.1758*** (0.0244)                    
## ANews                 -0.0005*** (0.0002)    -0.0011 (0.0008)
## NewsAverage               0.0001 (0.0003)    -0.0022 (0.0016)
## log(NewsCount)            0.0001 (0.0001) -0.0021*** (0.0006)
## log(Amihud_monthly)   -0.0021*** (0.0001) -0.0046*** (0.0007)
## OMRFlag                0.0017*** (0.0003)  0.0077*** (0.0016)
## l(RET_m1,1)           -0.0040*** (0.0005) -0.0121*** (0.0020)
## l(RET_m1,2)           -0.0016*** (0.0004)   -0.0033* (0.0017)
## l(RET_m1,3)              -0.0006 (0.0004)     0.0004 (0.0016)
## log(TA)                 -0.0008* (0.0004)     0.0008 (0.0020)
## CtA                      0.0018* (0.0008)   0.0132** (0.0040)
## EBITDAtA                 0.0050. (0.0028)     0.0093 (0.0119)
## Leverage                  0.0001 (0.0015)   -0.0180* (0.0071)
## log(BM)                0.0009*** (0.0001)  0.0033*** (0.0007)
## DivtoAsset               -0.0093 (0.0179)    -0.0699 (0.1087)
## l(log(MarCap),1)       -0.0012** (0.0004)   -0.0042* (0.0019)
## l(RepIntensity_vol,1)                      0.2026*** (0.0374)
## AIAC                                                         
## Fixed-Effects:        ------------------- -------------------
## Ticker                                Yes                 Yes
## time                                  Yes                 Yes
## _____________________ ___________________ ___________________
## S.E.: Clustered                by: Ticker          by: Ticker
## Observations                       39,470              39,470
## R2                                0.25698             0.29122
## Within R2                         0.05686             0.05566
## F-test (IV only)                   49.443              102.10
## Wald (IV only)                     26.339              53.354
## Wu-Hausman                         2.0885              7.5654
## Wu-Hausman, p-value               0.14842             0.00595
## 
##                       summary(fe_2slsC,.. summary(fe_2slsC_..
## Dependent Var.:              RepIntensity    RepIntensity_vol
##                                                              
## AIA                                                          
## l(RepIntensity,1)      0.1757*** (0.0244)                    
## ANews                 -0.0005*** (0.0002)    -0.0011 (0.0008)
## NewsAverage               9.2e-5 (0.0003)    -0.0024 (0.0016)
## log(NewsCount)            0.0001 (0.0001) -0.0021*** (0.0006)
## log(Amihud_monthly)   -0.0021*** (0.0001) -0.0046*** (0.0007)
## OMRFlag                0.0016*** (0.0003)  0.0077*** (0.0016)
## l(RET_m1,1)           -0.0040*** (0.0005) -0.0121*** (0.0020)
## l(RET_m1,2)           -0.0016*** (0.0004)   -0.0034* (0.0017)
## l(RET_m1,3)              -0.0006 (0.0004)     0.0003 (0.0016)
## log(TA)                 -0.0008* (0.0004)     0.0008 (0.0020)
## CtA                      0.0018* (0.0008)   0.0132** (0.0040)
## EBITDAtA                 0.0050. (0.0028)     0.0093 (0.0120)
## Leverage                  0.0002 (0.0015)   -0.0177* (0.0071)
## log(BM)                0.0009*** (0.0001)  0.0034*** (0.0007)
## DivtoAsset               -0.0096 (0.0180)    -0.0724 (0.1092)
## l(log(MarCap),1)       -0.0012** (0.0004)   -0.0041* (0.0019)
## l(RepIntensity_vol,1)                      0.2023*** (0.0374)
## AIAC                  -0.0008*** (0.0002) -0.0060*** (0.0008)
## Fixed-Effects:        ------------------- -------------------
## Ticker                                Yes                 Yes
## time                                  Yes                 Yes
## _____________________ ___________________ ___________________
## S.E.: Clustered                by: Ticker          by: Ticker
## Observations                       39,470              39,470
## R2                                0.25702             0.29138
## Within R2                         0.05692             0.05587
## F-test (IV only)                   48.645              102.73
## Wald (IV only)                     23.913              52.176
## Wu-Hausman                        0.41342              2.4605
## Wu-Hausman, p-value               0.52024             0.11675
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
feols(fml = RepIntensity ~ AIA + l(RepIntensity, 1) + 
        # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
        ANews + NewsAverage + NewsCount + 
        Amihud_monthly + OMRFlag + # log(1 + NewsCount) +
        # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
        # MarCap + Month + Volatility + TradeVol
        l(RET_m1, 1:3)+ log(TA) + log(CtA) + (EBITDAtA) + log(Leverage) + (BM) + DivtoAsset + 
        l(log(MarCap), 1) + d(Volatility,1) + l(Volatility, 1) + log(TradeVol)
      | Ticker + time , # + Ticker^Year 
      data = pdShaRep, 
      cluster = c("Ticker")) %>% 
  summary
## NOTE: 32,741 observations removed because of NA and infinite values (RHS: 32,741).
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 41,044 
## Fixed-effects: Ticker: 1,251,  time: 102
## Standard-errors: Clustered (Ticker) 
##                        Estimate  Std. Error   t value   Pr(>|t|)    
## AIA                -0.000643483 0.000098935 -6.504086 1.1277e-10 ***
## l(RepIntensity, 1)  0.174439322 0.023335328  7.475332 1.4433e-13 ***
## ANews              -0.000511469 0.000165684 -3.087018 2.0662e-03 ** 
## NewsAverage         0.000302765 0.000384873  0.786663 4.3163e-01    
## NewsCount          -0.000000228 0.000000310 -0.732900 4.6376e-01    
## Amihud_monthly      0.011311045 0.008981598  1.259358 2.0814e-01    
## OMRFlag             0.001579378 0.000282518  5.590366 2.7796e-08 ***
## l(RET_m1, 1)       -0.002875966 0.000460414 -6.246475 5.7440e-10 ***
## l(RET_m1, 2)       -0.001380887 0.000394502 -3.500329 4.8104e-04 ***
## l(RET_m1, 3)       -0.000713748 0.000368079 -1.939115 5.2712e-02 .  
## log(TA)            -0.000733340 0.000276439 -2.652808 8.0836e-03 ** 
## log(CtA)            0.000236589 0.000067028  3.529687 4.3116e-04 ***
## EBITDAtA            0.005574247 0.002665316  2.091402 3.6693e-02 *  
## log(Leverage)       0.000572836 0.000274811  2.084471 3.7320e-02 *  
## BM                  0.000167625 0.000207246  0.808825 4.1877e-01    
## DivtoAsset         -0.028233974 0.020976721 -1.345967 1.7856e-01    
## l(log(MarCap), 1)   0.000367131 0.000237969  1.542769 1.2314e-01    
## d(Volatility, 1)   -0.043794605 0.007211907 -6.072542 1.6677e-09 ***
## l(Volatility, 1)   -0.046947723 0.008905457 -5.271793 1.5903e-07 ***
## log(TradeVol)       0.001996389 0.000167365 11.928383  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005474     Adj. R2: 0.226266
##                  Within R2: 0.052337
feols(fml = RepIntensity ~ MarketAIA + l(RepIntensity, 1) 
      | Ticker + time, data = pdShaRep, cluster = "Ticker")
## NOTE: 12,149 observations removed because of NA values (RHS: 12,149).
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 61,636 
## Fixed-effects: Ticker: 1,526,  time: 128
## Standard-errors: Clustered (Ticker) 
##                    Estimate Std. Error t value   Pr(>|t|)    
## MarketAIA          0.621234   0.108842 5.70764 1.3742e-08 ***
## l(RepIntensity, 1) 0.187119   0.020638 9.06674  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005846     Adj. R2: 0.206696
##                  Within R2: 0.034047
feglm(fml = ShaRepYes ~ AIA + l(ShaRepYes, 1) + 
        # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
        ANews + NewsAverage + NewsCount + 
        Amihud_monthly + OMRFlag + # log(1 + NewsCount) +
        # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
        # MarCap + Month + Volatility + TradeVol
        l(RET_m1, 1:3)+ log(TA) + CtA + EBITDAtA + log(Leverage) + (BM) + DivtoAsset + 
        l(log(MarCap), 1) + d(Volatility,1) + l(Volatility, 1) + log(TradeVol)
      | Ticker + time , # + Ticker^Year 
      data = pdShaRep, family = binomial,
      cluster = c("Ticker"))
## NOTES: 32,698 observations removed because of NA values (RHS: 32,698).
##        328/0 fixed-effects (4,666 observations) removed because of only 0 (or only 1) outcomes.
## GLM estimation, family = binomial, Dep. Var.: ShaRepYes
## Observations: 36,421 
## Fixed-effects: Ticker: 923,  time: 102
## Standard-errors: Clustered (Ticker) 
##                  Estimate Std. Error   t value   Pr(>|t|)    
## AIA             -0.339306   0.054271 -6.252085 4.0501e-10 ***
## l(ShaRepYes, 1)  1.891207   0.066513 28.433574  < 2.2e-16 ***
## ANews           -0.210979   0.076097 -2.772506 5.5626e-03 ** 
## NewsAverage      0.264554   0.180525  1.465468 1.4279e-01    
## NewsCount       -0.000172   0.000190 -0.903192 3.6642e-01    
## Amihud_monthly  14.826788  11.187188  1.325337 1.8506e-01    
## OMRFlag          0.602179   0.125324  4.804962 1.5478e-06 ***
## l(RET_m1, 1)    -1.283040   0.227131 -5.648901 1.6148e-08 ***
## ... 12 coefficients remaining (display them with summary() or use argument n)
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Log-Likelihood: -15,260.9   Adj. Pseudo R2: 0.344347
##            BIC:  41,486.9     Squared Cor.: 0.451475
## 5. within-firm standard deviation ---- 
fe_2sls_log <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                   # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                   # MarCap + Month + Volatility + TradeVol
                   l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                   l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                 | Ticker + time | AIA ~ MarketAIA, 
                   # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                   # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                   # AIA:l(1-ShaRepYes, 1, fill = 0) + AIA:l(ShaRepYes, 1, fill = 0) ~ MarketAIA:l(1-ShaRepYes, 1, fill = 0) + MarketAIA:l(ShaRepYes, 1, fill = 0) , 
                   # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
                   # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                 data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                 # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
summary(fe_2sls_log, stage = 2)
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA, Instr.: MarketAIA
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA             -0.000564   0.000110  -5.132138 3.3273e-07 ***
## l(RepIntensity, 1)   0.175804   0.024377   7.211989 9.6171e-13 ***
## ANews               -0.000525   0.000155  -3.379464 7.4907e-04 ***
## NewsAverage          0.000131   0.000347   0.377680 7.0573e-01    
## log(NewsCount)       0.000111   0.000102   1.087722 2.7693e-01    
## log(Amihud_monthly) -0.002069   0.000150 -13.818555  < 2.2e-16 ***
## OMRFlag              0.001651   0.000297   5.562898 3.2538e-08 ***
## l(RET_m1, 1)        -0.004001   0.000478  -8.369848  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001564   0.000396  -3.944144 8.4615e-05 ***
## l(RET_m1, 3)        -0.000573   0.000373  -1.535225 1.2499e-01    
## log(TA)             -0.000848   0.000421  -2.015178 4.4104e-02 *  
## CtA                  0.001771   0.000764   2.319118 2.0552e-02 *  
## EBITDAtA             0.005004   0.002832   1.766994 7.7478e-02 .  
## Leverage             0.000123   0.001460   0.084518 9.3266e-01    
## log(BM)              0.000945   0.000139   6.816235 1.4614e-11 ***
## DivtoAsset          -0.009282   0.017855  -0.519857 6.0326e-01    
## l(log(MarCap), 1)   -0.001178   0.000386  -3.049153 2.3440e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230749
##                  Within R2: 0.056862
## F-test (1st stage), AIA: stat = 211,915.5    , p < 2.2e-16 , on 1 and 39,351 DoF.
##              Wu-Hausman: stat =       2.08848, p = 0.148421, on 1 and 38,122 DoF.
# iplot(fe_2sls_log)

fe_2sls_log2 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
                       # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                       ANews + NewsAverage + log(NewsCount) + 
                       OMRFlag + # log(1 + NewsCount) +
                       # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                       # MarCap + Month + Volatility + TradeVol
                       l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                       l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                     | Ticker + time | AIA ~ MarketAIA , #  + Ticker^yearqtr(YM)
                     data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                     # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                     cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
#### 5.1 within-firm standard deviation ---- 
mm <- feols(fml = # AIA ~ 1 
            AIA ~ 1 # log(Amihud_monthly)
            | Ticker + time, # + Ticker^year(YM), 
            data = pdShaRep, # [pdShaRep$ShaRepYes == T,], 
            cluster = c("Ticker"))
sqrt(sum((mm$residuals)^2) / (nrow(pdShaRep) - length(unique(pdShaRep$Ticker))))
## [1] 0.4251317
## 6. Logit model ---- 
fe_prob <- feglm(fml = ShaRepYes ~ AIA + l(ShaRepYes, 1) + 
           # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
           ANews + NewsAverage + log(NewsCount) + 
           log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
           # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
           # MarCap + Month + Volatility + TradeVol
           l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
           l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) # + log(TradeVol) # + lambda
       | Ticker + time, # | AIA ~ MarketAIA , #  + Ticker^yearqtr(YM)
       data = pdShaRep, family = gaussian(link = "identity"), #binomial(link = 'logit'),
       cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
fe_prob
## GLM estimation, family = gaussian(link = "identity"), Dep. Var.: ShaRepYes
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error  t value   Pr(>|t|)    
## AIA                 -0.032552   0.006132 -5.30881 1.3085e-07 ***
## l(ShaRepYes, 1)      0.365259   0.012394 29.47160  < 2.2e-16 ***
## ANews               -0.022815   0.008917 -2.55862 1.0628e-02 *  
## NewsAverage          0.046772   0.017975  2.60198 9.3803e-03 ** 
## log(NewsCount)      -0.009222   0.006198 -1.48782 1.3705e-01    
## log(Amihud_monthly) -0.056668   0.008076 -7.01674 3.7449e-12 ***
## OMRFlag              0.081345   0.014667  5.54597 3.5764e-08 ***
## l(RET_m1, 1)        -0.147712   0.025826 -5.71955 1.3403e-08 ***
## ... 9 coefficients remaining (display them with summary() or use argument n)
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Log-Likelihood: -14,557.5   Adj. Pseudo R2: 0.442167
##            BIC:  43,370.6     Squared Cor.: 0.50686
fe_probC <- feglm(fml = ShaRepYes ~ AIAC + l(ShaRepYes, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
                   # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                   # MarCap + Month + Volatility + TradeVol
                   l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                   l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) # + log(TradeVol) # + lambda
                 | Ticker + time, # | AIA ~ MarketAIA , #  + Ticker^yearqtr(YM)
                 data = pdShaRep, family = gaussian(link = "identity"), #binomial(link = 'logit'),
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
fe_prob_2sls <- feols(fml = ShaRepYes ~ l(ShaRepYes, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
                   # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                   # MarCap + Month + Volatility + TradeVol
                   l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                   l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) # + log(TradeVol) # + lambda
                 | Ticker + time | AIA ~ MarketAIA , #  + Ticker^yearqtr(YM)
                 data = pdShaRep, #binomial(link = 'logit'),
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
fe_probC_2sls <- feols(fml = ShaRepYes ~ l(ShaRepYes, 1) + 
                        # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                        ANews + NewsAverage + log(NewsCount) + 
                        log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
                        # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                        # MarCap + Month + Volatility + TradeVol
                        l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                        l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) # + log(TradeVol) # + lambda
                      | Ticker + time | AIAC ~ MarketAIAC , #  + Ticker^yearqtr(YM)
                      data = pdShaRep, 
                      cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
etable(fe_prob, fe_probC, 
       summary(fe_prob_2sls, stage = 2),
       summary(fe_probC_2sls, stage = 2),
       fitstat = ~ . + ivfall + ivwaldall + wh + wh.p, 
       tex = T) 
## \begingroup
## \centering
## \begin{tabular}{lcccc}
##    \tabularnewline \midrule \midrule
##    Dependent Variable: & \multicolumn{4}{c}{ShaRepYes}\\
##    Model:                & (1)                   & (2)                  & (3)             & (4)\\  
##                          &  gaussian("identity") & gaussian("identity") & OLS             & OLS\\  
##    \midrule
##    \emph{Variables}\\
##    AIA                   & -0.0326$^{***}$       &                      & -0.0341$^{***}$ &   \\   
##                          & (0.0061)              &                      & (0.0070)        &   \\   
##    l(ShaRepYes,1)        & 0.3653$^{***}$        & 0.3651$^{***}$       & 0.3653$^{***}$  & 0.3651$^{***}$\\   
##                          & (0.0124)              & (0.0124)             & (0.0124)        & (0.0124)\\   
##    ANews                 & -0.0228$^{**}$        & -0.0227$^{**}$       & -0.0227$^{**}$  & -0.0226$^{**}$\\   
##                          & (0.0089)              & (0.0089)             & (0.0089)        & (0.0089)\\   
##    NewsAverage           & 0.0468$^{***}$        & 0.0447$^{**}$        & 0.0475$^{***}$  & 0.0449$^{**}$\\   
##                          & (0.0180)              & (0.0179)             & (0.0179)        & (0.0179)\\   
##    log(NewsCount)        & -0.0092               & -0.0090              & -0.0090         & -0.0090\\   
##                          & (0.0062)              & (0.0062)             & (0.0062)        & (0.0062)\\   
##    log(Amihud\_monthly)  & -0.0567$^{***}$       & -0.0573$^{***}$      & -0.0567$^{***}$ & -0.0573$^{***}$\\   
##                          & (0.0081)              & (0.0081)             & (0.0081)        & (0.0081)\\   
##    OMRFlag               & 0.0813$^{***}$        & 0.0812$^{***}$       & 0.0814$^{***}$  & 0.0812$^{***}$\\   
##                          & (0.0147)              & (0.0147)             & (0.0147)        & (0.0147)\\   
##    l(RET\_m1,1)          & -0.1477$^{***}$       & -0.1476$^{***}$      & -0.1479$^{***}$ & -0.1477$^{***}$\\   
##                          & (0.0258)              & (0.0258)             & (0.0258)        & (0.0258)\\   
##    l(RET\_m1,2)          & -0.0553$^{**}$        & -0.0560$^{***}$      & -0.0554$^{**}$  & -0.0560$^{***}$\\   
##                          & (0.0216)              & (0.0216)             & (0.0216)        & (0.0216)\\   
##    l(RET\_m1,3)          & -0.0338               & -0.0347$^{*}$        & -0.0339         & -0.0347$^{*}$\\   
##                          & (0.0210)              & (0.0210)             & (0.0210)        & (0.0210)\\   
##    log(TA)               & -0.0896$^{***}$       & -0.0895$^{***}$      & -0.0896$^{***}$ & -0.0895$^{***}$\\   
##                          & (0.0290)              & (0.0290)             & (0.0290)        & (0.0290)\\   
##    CtA                   & -0.0384               & -0.0386              & -0.0382         & -0.0385\\   
##                          & (0.0516)              & (0.0516)             & (0.0516)        & (0.0516)\\   
##    EBITDAtA              & 0.3243                & 0.3246               & 0.3239          & 0.3245\\   
##                          & (0.2363)              & (0.2371)             & (0.2364)        & (0.2371)\\   
##    Leverage              & -0.0718               & -0.0692              & -0.0714         & -0.0690\\   
##                          & (0.0932)              & (0.0932)             & (0.0932)        & (0.0933)\\   
##    log(BM)               & 0.0383$^{***}$        & 0.0384$^{***}$       & 0.0384$^{***}$  & 0.0384$^{***}$\\   
##                          & (0.0091)              & (0.0091)             & (0.0091)        & (0.0091)\\   
##    DivtoAsset            & 0.1992                & 0.1801               & 0.1981          & 0.1792\\   
##                          & (1.602)               & (1.607)              & (1.602)         & (1.607)\\   
##    l(log(MarCap),1)      & 0.0358                & 0.0363               & 0.0360          & 0.0363\\   
##                          & (0.0239)              & (0.0239)             & (0.0239)        & (0.0239)\\   
##    AIAC                  &                       & -0.0451$^{***}$      &                 & -0.0460$^{***}$\\   
##                          &                       & (0.0091)             &                 & (0.0098)\\   
##    \midrule
##    \emph{Fixed-effects}\\
##    Ticker                & Yes                   & Yes                  & Yes             & Yes\\  
##    time                  & Yes                   & Yes                  & Yes             & Yes\\  
##    \midrule
##    \emph{Fit statistics}\\
##    Observations          & 39,470                & 39,470               & 39,470          & 39,470\\  
##    Squared Correlation   & 0.50686               & 0.50683              & 0.50682         & 0.50680\\  
##    Pseudo R$^2$          & 0.48938               & 0.48934              & 0.48939         & 0.48936\\  
##    BIC                   & 43,370.6              & 43,372.7             & 43,368.7        & 43,370.8\\  
##    F-test (IV only)      &                       &                      & 43.054          & 41.382\\  
##    Wald (IV only)        &                       &                      & 23.945          & 22.127\\  
##    Wu-Hausman            &                       &                      & 0.53937         & 0.15367\\  
##    Wu-Hausman, p-value   &                       &                      & 0.46270         & 0.69506\\  
##    \midrule \midrule
##    \multicolumn{5}{l}{\emph{Clustered (Ticker) standard-errors in parentheses}}\\
##    \multicolumn{5}{l}{\emph{Signif. Codes: ***: 0.01, **: 0.05, *: 0.1}}\\
## \end{tabular}
## \par\endgroup
## 7. subgroup analysis ----- 

pdShaRep <- panel(ShaRep_AIA_merge_illiquidity_OMR_CCM_c2_summary %>% 
                    # mutate(reporting_ym = as.yearmon(reporting), 
                    #        filing_ym = as.yearmon(filing)) %>% 
                    filter(RepIntensity <= 0.10) %>% 
                    mutate(TradeVol_shaout = TradeVol / ShaOut) %>% 
                    group_by(YM) %>% 
                    mutate(BM_q1 = quantile(BM, na.rm = T)[2],
                           BM_q2 = quantile(BM, na.rm = T)[3],
                           BM_q3 = quantile(BM, na.rm = T)[4],
                           BM_q4 = quantile(BM, na.rm = T)[5],
                           RET_md = median(RET_m1, na.rm = T), 
                           RET_mean = mean(RET_m1, na.rm = T), 
                           frequency = mean(ShaRepYes, na.rm = T),
                           Volatility_md = median(Volatility, na.rm = T)
                    ) %>% 
                    ungroup() %>% 
                    mutate(UnderPriced = BM > BM_q2,
                           BM_middle = (BM >= BM_q1) & (BM <= BM_q3) ,
                           PriceQ1 = 1*(BM <= BM_q1), 
                           PriceQ2 = 2*(BM > BM_q1 & BM <= BM_q2), 
                           PriceQ3 = 3*(BM > BM_q2 & BM <= BM_q3), 
                           PriceQ4 = 4*(BM > BM_q3 & BM <= BM_q4), 
                           PriceQ = PriceQ1 + PriceQ2 + PriceQ3 + PriceQ4, 
                           HighVolatility = Volatility > Volatility_md, 
                           RET_m1_0 = RET_m1 > 0, 
                    ) %>% 
                    mutate(YQ = yearqtr(YM))# %>% 
                  #mutate(group1 = (wv_bhar_reb1 > 0) + (wv_bhar_reb0 > 0), 
                  #       group3 = (wv_bhar_reb3 > 0) + (wv_bhar_reb0 > 0),
                  #       group6 = (wv_bhar_reb6 > 0) + (wv_bhar_reb0 > 0)
                  # )
                  , ~ Ticker + time)
names(pdShaRep)
##  [1] "YM"               "AIAC"             "ANews"            "NewsAverage"     
##  [5] "NewsCount"        "MarketAIA"        "MarketAIAC"       "CUSIP"           
##  [9] "CIK"              "gvkey"            "Name"             "cusip8"          
## [13] "CUSIP_tts"        "AIA"              "ShaRep3"          "missing3"        
## [17] "Price2"           "Amihud_monthly"   "OMRFlag"          "Ticker"          
## [21] "RET_m1"           "Volatility"       "AvePrice"         "TradeVol"        
## [25] "TradeVolDollar"   "MarCap"           "ShaOut"           "ShaOutPrevious"  
## [29] "datadate"         "tic"              "cusip"            "atq"             
## [33] "ceqq"             "cheq"             "oibdpq"           "pstkq"           
## [37] "seqq"             "txditcq"          "cdvcy"            "costat"          
## [41] "dlcq"             "dlttq"            "BE"               "TD"              
## [45] "CtA"              "TA"               "Year"             "Quarter"         
## [49] "Month"            "RepIntensity"     "RepIntensity_vol" "ShaRepYes"       
## [53] "BM"               "DivtoAsset"       "EBITDA"           "Leverage"        
## [57] "TradeVol_scaled"  "EBITDAtA"         "time"             "sic"             
## [61] "shortintadj"      "OMR_YM"           "ProgramMonth"     "ShortInterest"   
## [65] "wv_bhar_reb3"     "wv_bhar_nreb3"    "wv_bhar_reb6"     "wv_bhar_nreb6"   
## [69] "wv_bhar_reb1"     "wv_bhar_nreb1"    "wv_bhar_reb0"     "wv_bhar_nreb0"   
## [73] "TradeVol_shaout"  "BM_q1"            "BM_q2"            "BM_q3"           
## [77] "BM_q4"            "RET_md"           "RET_mean"         "frequency"       
## [81] "Volatility_md"    "UnderPriced"      "BM_middle"        "PriceQ1"         
## [85] "PriceQ2"          "PriceQ3"          "PriceQ4"          "PriceQ"          
## [89] "HighVolatility"   "RET_m1_0"         "YQ"
fe_2sls_underpriced <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(l(UnderPriced, 1)) + 
                       # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                       ANews + NewsAverage + log(NewsCount) + 
                       log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                       # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                       # MarCap + Month + Volatility + TradeVol
                       l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + l(log(BM), 1) + (DivtoAsset) + 
                       l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                     | Ticker + time | # AIA ~ MarketAIA, 
                     # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                     AIA:i(l(UnderPriced, 1)) ~ MarketAIA:i(l(UnderPriced, 1)), ## UnderPriced versus Overpriced   
                     # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                     # AIA:l(1-ShaRepYes, 1, fill = 0) + AIA:l(ShaRepYes, 1, fill = 0) ~ MarketAIA:l(1-ShaRepYes, 1, fill = 0) + MarketAIA:l(ShaRepYes, 1, fill = 0) , 
                     # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
                     # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                     data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                     # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                     cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,312 observations removed because of NA and infinite values (RHS: 34,312, IV: 12,591/12,591).
fe_2sls_underpriced
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:i(l(UnderPriced, 1)), Instr.: MarketAIA:i(l(UnderPriced, 1))
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,473 
## Fixed-effects: Ticker: 1,230,  time: 102
## Standard-errors: Clustered (Ticker) 
##                                   Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA:l(UnderPriced, 1)::FALSE -0.000255   0.000259  -0.983928 3.2534e-01    
## fit_AIA:l(UnderPriced, 1)::TRUE  -0.000860   0.000258  -3.328963 8.9754e-04 ***
## l(RepIntensity, 1)                0.174519   0.024252   7.196134 1.0748e-12 ***
## l(UnderPriced, 1)::TRUE           0.000863   0.000371   2.323916 2.0292e-02 *  
## ANews                            -0.000529   0.000154  -3.444221 5.9200e-04 ***
## NewsAverage                       0.000057   0.000338   0.169977 8.6506e-01    
## log(NewsCount)                    0.000128   0.000104   1.230235 2.1884e-01    
## log(Amihud_monthly)              -0.002050   0.000148 -13.810363  < 2.2e-16 ***
## OMRFlag                           0.001638   0.000298   5.491618 4.8353e-08 ***
## l(RET_m1, 1)                     -0.004426   0.000486  -9.108216  < 2.2e-16 ***
## l(RET_m1, 2)                     -0.001577   0.000398  -3.959045 7.9565e-05 ***
## l(RET_m1, 3)                     -0.000566   0.000374  -1.511670 1.3088e-01    
## log(TA)                          -0.000563   0.000421  -1.337008 1.8147e-01    
## CtA                               0.001840   0.000759   2.424386 1.5478e-02 *  
## EBITDAtA                          0.005006   0.002819   1.775733 7.6024e-02 .  
## Leverage                         -0.000513   0.001472  -0.348733 7.2735e-01    
## l(log(BM), 1)                     0.000608   0.000132   4.605769 4.5367e-06 ***
## DivtoAsset                       -0.011642   0.018233  -0.638535 5.2324e-01    
## l(log(MarCap), 1)                -0.001397   0.000384  -3.643520 2.8015e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005418     Adj. R2: 0.229254
##                  Within R2: 0.055888
## F-test (1st stage), AIA:l(UnderPriced, 1)::FALSE: stat = 11,775.9  , p < 2.2e-16 , on 2 and 39,352 DoF.
## F-test (1st stage), AIA:l(UnderPriced, 1)::TRUE : stat = 10,488.1  , p < 2.2e-16 , on 2 and 39,352 DoF.
##                                       Wu-Hausman: stat =      1.673, p = 0.187697, on 2 and 38,121 DoF.
{
  fe_2sls_underpriced2 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + (l(UnderPriced, 1)) + 
                                 # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                                 ANews + NewsAverage + log(NewsCount) + 
                                 log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                                 # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                                 # MarCap + Month + Volatility + TradeVol
                                 l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + l(log(BM), 1) + (DivtoAsset) + 
                                 l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                               | Ticker + time | # AIA ~ MarketAIA, 
                                 # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                                 AIA + AIA:(l(UnderPriced, 1)) ~ MarketAIA + MarketAIA:(l(UnderPriced, 1)), ## UnderPriced versus Overpriced   
                               # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                               # AIA:l(1-ShaRepYes, 1, fill = 0) + AIA:l(ShaRepYes, 1, fill = 0) ~ MarketAIA:l(1-ShaRepYes, 1, fill = 0) + MarketAIA:l(ShaRepYes, 1, fill = 0) , 
                               # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
                               # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                               data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                               # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                               cluster = c("Ticker"))
  fe_2sls_underpriced2 
  
  fe_2sls_underpriced3 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + (l(BM_middle, 1)) + 
                                  # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                                  ANews + NewsAverage + log(NewsCount) + 
                                  log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                                  # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                                  # MarCap + Month + Volatility + TradeVol
                                  l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + l(log(BM), 1) + (DivtoAsset) + 
                                  l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                                | Ticker + time | # AIA ~ MarketAIA, 
                                  # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                                  AIA:(l(BM_middle, 1)) ~ MarketAIA:(l(BM_middle, 1)), ## UnderPriced versus Overpriced   
                                # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                                # AIA:l(1-ShaRepYes, 1, fill = 0) + AIA:l(ShaRepYes, 1, fill = 0) ~ MarketAIA:l(1-ShaRepYes, 1, fill = 0) + MarketAIA:l(ShaRepYes, 1, fill = 0) , 
                                # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
                                # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                                data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                                # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                                cluster = c("Ticker"))
  fe_2sls_underpriced3 
  
  
  
  pdShaRep %>% group_by(UnderPriced %in% c(T, F)) %>% summarise(RepFrequency = mean(ShaRepYes, na.rm = T))
  feols(fml = ShaRep3 ~ i(UnderPriced) | Ticker + time, data = pdShaRep)
  pdShaRep %>% group_by((ShaRepYes)) %>% summarise(RepFrequency = mean(ShaRepYes, na.rm = T))
  feols(fml = ShaRep3 ~ i(l(ShaRepYes, 1, fill = NA)) | Ticker + time, data = pdShaRep)
}
## Warning in log(BM): NaNs produced
## NOTE: 34,312 observations removed because of NA and infinite values (RHS: 34,312, IV: 12,591/12,591).
## Warning in log(BM): NaNs produced
## NOTE: 34,312 observations removed because of NA and infinite values (RHS: 34,312, IV: 12,591/12,591).
## NOTE: 540 observations removed because of NA values (RHS: 540).
## NOTE: 12,149 observations removed because of NA values (RHS: 12,149).
## OLS estimation, Dep. Var.: ShaRep3
## Observations: 61,636 
## Fixed-effects: Ticker: 1,526,  time: 128
## Standard-errors: Clustered (Ticker) 
##                               Estimate Std. Error t value   Pr(>|t|)    
## l(ShaRepYes, 1, fill = NA)::1 0.617227   0.099553 6.20001 7.2537e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 3.44117     Adj. R2: 0.363998
##                 Within R2: 0.004757
fe_2sls_sharepprevious <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(l(ShaRepYes, 1, fill = NA)) + 
                               # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                               ANews + NewsAverage + log(NewsCount) + 
                               log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                               # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                               # MarCap + Month + Volatility + TradeVol
                               l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                               l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                             | Ticker + time | # AIA ~ MarketAIA, 
                               # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                               # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                             AIA:i(l(ShaRepYes, 1, fill = NA)) ~ MarketAIA:i(l(ShaRepYes, 1, fill = NA)) , 
                             # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
                             # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                             data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                             # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                             cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315, IV: 12,149/12,149).
fe_2sls_sharepprevious
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:i(l(ShaRepYes, 1, fill = NA)), Instr.: MarketAIA:i(l(ShaRepYes, 1, fill = NA))
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                                        Estimate Std. Error    t value
## fit_AIA:l(ShaRepYes, 1, fill = NA)::0 -0.000764   0.000246  -3.098300
## fit_AIA:l(ShaRepYes, 1, fill = NA)::1 -0.000427   0.000209  -2.041947
## l(RepIntensity, 1)                     0.151612   0.025979   5.836051
## l(ShaRepYes, 1, fill = NA)::1          0.000625   0.000317   1.972282
## ANews                                 -0.000523   0.000158  -3.315550
## NewsAverage                            0.000108   0.000354   0.305681
## log(NewsCount)                         0.000153   0.000101   1.508543
## log(Amihud_monthly)                   -0.002080   0.000150 -13.871720
## OMRFlag                                0.001608   0.000297   5.421542
## l(RET_m1, 1)                          -0.003949   0.000473  -8.341176
## l(RET_m1, 2)                          -0.001487   0.000395  -3.761115
## l(RET_m1, 3)                          -0.000523   0.000372  -1.408898
## log(TA)                               -0.000767   0.000412  -1.861296
## CtA                                    0.001914   0.000753   2.540355
## EBITDAtA                               0.004457   0.002761   1.614532
## Leverage                               0.000242   0.001432   0.168886
## log(BM)                                0.000918   0.000137   6.700045
## DivtoAsset                            -0.009011   0.017564  -0.513032
## l(log(MarCap), 1)                     -0.001277   0.000385  -3.319349
##                                         Pr(>|t|)    
## fit_AIA:l(ShaRepYes, 1, fill = NA)::0 1.9905e-03 ** 
## fit_AIA:l(ShaRepYes, 1, fill = NA)::1 4.1370e-02 *  
## l(RepIntensity, 1)                    6.8320e-09 ***
## l(ShaRepYes, 1, fill = NA)::1         4.8801e-02 *  
## ANews                                 9.4135e-04 ***
## NewsAverage                           7.5990e-01    
## log(NewsCount)                        1.3167e-01    
## log(Amihud_monthly)                    < 2.2e-16 ***
## OMRFlag                               7.1080e-08 ***
## l(RET_m1, 1)                           < 2.2e-16 ***
## l(RET_m1, 2)                          1.7713e-04 ***
## l(RET_m1, 3)                          1.5912e-01    
## log(TA)                               6.2941e-02 .  
## CtA                                   1.1196e-02 *  
## EBITDAtA                              1.0667e-01    
## Leverage                              8.6591e-01    
## log(BM)                               3.1657e-11 ***
## DivtoAsset                            6.0802e-01    
## l(log(MarCap), 1)                     9.2875e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005399     Adj. R2: 0.232913
##                  Within R2: 0.059564
## F-test (1st stage), AIA:l(ShaRepYes, 1, fill = NA)::0: stat =  5,956.3   , p < 2.2e-16, on 2 and 39,349 DoF.
## F-test (1st stage), AIA:l(ShaRepYes, 1, fill = NA)::1: stat = 12,407.4   , p < 2.2e-16, on 2 and 39,349 DoF.
##                                            Wu-Hausman: stat =      1.5813, p = 0.20572, on 2 and 38,119 DoF.
{
    feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(l(ShaRepYes, 1, fill = NA)) + 
        ANews + NewsAverage + log(NewsCount) + 
        log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
        l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
        l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
        | Ticker + time | # AIA ~ MarketAIA, 
        # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
        # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
        AIA:i(l(ShaRepYes, 1, fill = NA)) ~ MarketAIA:i(l(ShaRepYes, 1, fill = NA)) , 
        # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
        # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
        data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
        # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
        cluster = c("Ticker"))
}
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315, IV: 12,149/12,149).
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:i(l(ShaRepYes, 1, fill = NA)), Instr.: MarketAIA:i(l(ShaRepYes, 1, fill = NA))
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                                        Estimate Std. Error    t value
## fit_AIA:l(ShaRepYes, 1, fill = NA)::0 -0.000764   0.000246  -3.098300
## fit_AIA:l(ShaRepYes, 1, fill = NA)::1 -0.000427   0.000209  -2.041947
## l(RepIntensity, 1)                     0.151612   0.025979   5.836051
## l(ShaRepYes, 1, fill = NA)::1          0.000625   0.000317   1.972282
## ANews                                 -0.000523   0.000158  -3.315550
## NewsAverage                            0.000108   0.000354   0.305681
## log(NewsCount)                         0.000153   0.000101   1.508543
## log(Amihud_monthly)                   -0.002080   0.000150 -13.871720
## OMRFlag                                0.001608   0.000297   5.421542
## l(RET_m1, 1)                          -0.003949   0.000473  -8.341176
## l(RET_m1, 2)                          -0.001487   0.000395  -3.761115
## l(RET_m1, 3)                          -0.000523   0.000372  -1.408898
## log(TA)                               -0.000767   0.000412  -1.861296
## CtA                                    0.001914   0.000753   2.540355
## EBITDAtA                               0.004457   0.002761   1.614532
## Leverage                               0.000242   0.001432   0.168886
## log(BM)                                0.000918   0.000137   6.700045
## DivtoAsset                            -0.009011   0.017564  -0.513032
## l(log(MarCap), 1)                     -0.001277   0.000385  -3.319349
##                                         Pr(>|t|)    
## fit_AIA:l(ShaRepYes, 1, fill = NA)::0 1.9905e-03 ** 
## fit_AIA:l(ShaRepYes, 1, fill = NA)::1 4.1370e-02 *  
## l(RepIntensity, 1)                    6.8320e-09 ***
## l(ShaRepYes, 1, fill = NA)::1         4.8801e-02 *  
## ANews                                 9.4135e-04 ***
## NewsAverage                           7.5990e-01    
## log(NewsCount)                        1.3167e-01    
## log(Amihud_monthly)                    < 2.2e-16 ***
## OMRFlag                               7.1080e-08 ***
## l(RET_m1, 1)                           < 2.2e-16 ***
## l(RET_m1, 2)                          1.7713e-04 ***
## l(RET_m1, 3)                          1.5912e-01    
## log(TA)                               6.2941e-02 .  
## CtA                                   1.1196e-02 *  
## EBITDAtA                              1.0667e-01    
## Leverage                              8.6591e-01    
## log(BM)                               3.1657e-11 ***
## DivtoAsset                            6.0802e-01    
## l(log(MarCap), 1)                     9.2875e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005399     Adj. R2: 0.232913
##                  Within R2: 0.059564
## F-test (1st stage), AIA:l(ShaRepYes, 1, fill = NA)::0: stat =  5,956.3   , p < 2.2e-16, on 2 and 39,349 DoF.
## F-test (1st stage), AIA:l(ShaRepYes, 1, fill = NA)::1: stat = 12,407.4   , p < 2.2e-16, on 2 and 39,349 DoF.
##                                            Wu-Hausman: stat =      1.5813, p = 0.20572, on 2 and 38,119 DoF.
fe_2sls_sharepprevious
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:i(l(ShaRepYes, 1, fill = NA)), Instr.: MarketAIA:i(l(ShaRepYes, 1, fill = NA))
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                                        Estimate Std. Error    t value
## fit_AIA:l(ShaRepYes, 1, fill = NA)::0 -0.000764   0.000246  -3.098300
## fit_AIA:l(ShaRepYes, 1, fill = NA)::1 -0.000427   0.000209  -2.041947
## l(RepIntensity, 1)                     0.151612   0.025979   5.836051
## l(ShaRepYes, 1, fill = NA)::1          0.000625   0.000317   1.972282
## ANews                                 -0.000523   0.000158  -3.315550
## NewsAverage                            0.000108   0.000354   0.305681
## log(NewsCount)                         0.000153   0.000101   1.508543
## log(Amihud_monthly)                   -0.002080   0.000150 -13.871720
## OMRFlag                                0.001608   0.000297   5.421542
## l(RET_m1, 1)                          -0.003949   0.000473  -8.341176
## l(RET_m1, 2)                          -0.001487   0.000395  -3.761115
## l(RET_m1, 3)                          -0.000523   0.000372  -1.408898
## log(TA)                               -0.000767   0.000412  -1.861296
## CtA                                    0.001914   0.000753   2.540355
## EBITDAtA                               0.004457   0.002761   1.614532
## Leverage                               0.000242   0.001432   0.168886
## log(BM)                                0.000918   0.000137   6.700045
## DivtoAsset                            -0.009011   0.017564  -0.513032
## l(log(MarCap), 1)                     -0.001277   0.000385  -3.319349
##                                         Pr(>|t|)    
## fit_AIA:l(ShaRepYes, 1, fill = NA)::0 1.9905e-03 ** 
## fit_AIA:l(ShaRepYes, 1, fill = NA)::1 4.1370e-02 *  
## l(RepIntensity, 1)                    6.8320e-09 ***
## l(ShaRepYes, 1, fill = NA)::1         4.8801e-02 *  
## ANews                                 9.4135e-04 ***
## NewsAverage                           7.5990e-01    
## log(NewsCount)                        1.3167e-01    
## log(Amihud_monthly)                    < 2.2e-16 ***
## OMRFlag                               7.1080e-08 ***
## l(RET_m1, 1)                           < 2.2e-16 ***
## l(RET_m1, 2)                          1.7713e-04 ***
## l(RET_m1, 3)                          1.5912e-01    
## log(TA)                               6.2941e-02 .  
## CtA                                   1.1196e-02 *  
## EBITDAtA                              1.0667e-01    
## Leverage                              8.6591e-01    
## log(BM)                               3.1657e-11 ***
## DivtoAsset                            6.0802e-01    
## l(log(MarCap), 1)                     9.2875e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005399     Adj. R2: 0.232913
##                  Within R2: 0.059564
## F-test (1st stage), AIA:l(ShaRepYes, 1, fill = NA)::0: stat =  5,956.3   , p < 2.2e-16, on 2 and 39,349 DoF.
## F-test (1st stage), AIA:l(ShaRepYes, 1, fill = NA)::1: stat = 12,407.4   , p < 2.2e-16, on 2 and 39,349 DoF.
##                                            Wu-Hausman: stat =      1.5813, p = 0.20572, on 2 and 38,119 DoF.
# fitstat(fe_2sls_sharepprevious, ~ wh, cluster = 'Ticker')

fe_2sls_carm0 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + RET_m1_0 + # i(l(RET_m1 > RET_mean,-1)) + 
                               # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                               ANews + NewsAverage + log(NewsCount) + 
                               log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                               # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                               # MarCap + Month + Volatility + TradeVol
                               l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                               l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                             | Ticker + time | # AIA ~ MarketAIA, 
                               # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                               # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                               # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                             AIA:RET_m1_0 ~ MarketAIA:RET_m1_0 , 
                             # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                             data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                             # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                             cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,317 observations removed because of NA and infinite values (RHS: 34,317, IV: 4/4).
summary(fe_2sls_carm0, stage = 2)
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:RET_m1_0, Instr.: MarketAIA:RET_m1_0
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,468 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                        Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA:RET_m1_0FALSE -0.000781   0.000254  -3.079899 2.1167e-03 ** 
## fit_AIA:RET_m1_0TRUE  -0.000404   0.000228  -1.774606 7.6211e-02 .  
## l(RepIntensity, 1)     0.175884   0.024369   7.217459 9.2533e-13 ***
## RET_m1_0TRUE          -0.000614   0.000336  -1.826963 6.7948e-02 .  
## ANews                 -0.000508   0.000156  -3.266247 1.1199e-03 ** 
## NewsAverage            0.000106   0.000346   0.306268 7.5945e-01    
## log(NewsCount)         0.000111   0.000101   1.099756 2.7165e-01    
## log(Amihud_monthly)   -0.002112   0.000150 -14.046577  < 2.2e-16 ***
## OMRFlag                0.001655   0.000297   5.575364 3.0346e-08 ***
## l(RET_m1, 1)          -0.004156   0.000486  -8.555709  < 2.2e-16 ***
## l(RET_m1, 2)          -0.001557   0.000397  -3.919960 9.3455e-05 ***
## l(RET_m1, 3)          -0.000571   0.000373  -1.530755 1.2609e-01    
## log(TA)               -0.000569   0.000433  -1.313558 1.8924e-01    
## CtA                    0.001758   0.000765   2.298310 2.1712e-02 *  
## EBITDAtA               0.005379   0.002855   1.884324 5.9757e-02 .  
## Leverage              -0.000859   0.001512  -0.567879 5.7022e-01    
## log(BM)                0.000864   0.000138   6.256478 5.4280e-10 ***
## DivtoAsset            -0.008536   0.018372  -0.464632 6.4228e-01    
## l(log(MarCap), 1)     -0.001505   0.000399  -3.777571 1.6595e-04 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005406     Adj. R2: 0.230789
##                  Within R2: 0.056959
## F-test (1st stage), AIA:RET_m1_0FALSE: stat = 5,085.3    , p < 2.2e-16 , on 2 and 39,347 DoF.
## F-test (1st stage), AIA:RET_m1_0TRUE : stat = 6,840.4    , p < 2.2e-16 , on 2 and 39,347 DoF.
##                            Wu-Hausman: stat =     1.61054, p = 0.199793, on 2 and 38,117 DoF.
fe_2sls_carm3 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(l(log(1 + RET_m1),0:-3) > 0) + 
                         # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                         ANews + NewsAverage + log(NewsCount) + 
                         log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                         # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                         # MarCap + Month + Volatility + TradeVol
                         l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                         l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                       | Ticker + time | # AIA ~ MarketAIA, 
                         # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                         # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                         # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                         # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
                       AIA:i(l(log(1 + RET_m1),0:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),0:-3) > 0 ), 
                       data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                       # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                       cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 52,179 observations removed because of NA and infinite values (RHS: 52,179, IV: 32,057/32,057).
fe_2sls_carm3 
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:i(log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0), Instr.: MarketAIA:i(log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0)
## Second stage: Dep. Var.: RepIntensity
## Observations: 21,606 
## Fixed-effects: Ticker: 1,000,  time: 66
## Standard-errors: Clustered (Ticker) 
##                                                                                                             Estimate
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::FALSE -0.000884
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE  -0.000471
## l(RepIntensity, 1)                                                                                          0.163362
## log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE          -0.000401
## ANews                                                                                                      -0.000259
## NewsAverage                                                                                                 0.000071
## log(NewsCount)                                                                                             -0.000081
## log(Amihud_monthly)                                                                                        -0.002042
## OMRFlag                                                                                                     0.001584
## l(RET_m1, 1)                                                                                               -0.003801
## l(RET_m1, 2)                                                                                               -0.001212
## l(RET_m1, 3)                                                                                               -0.000551
## log(TA)                                                                                                    -0.000978
## CtA                                                                                                         0.002033
## EBITDAtA                                                                                                    0.004483
## Leverage                                                                                                    0.001363
## log(BM)                                                                                                     0.000897
## DivtoAsset                                                                                                  0.049638
## l(log(MarCap), 1)                                                                                          -0.000983
##                                                                                                            Std. Error
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::FALSE   0.000431
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE    0.000284
## l(RepIntensity, 1)                                                                                           0.026118
## log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE            0.000539
## ANews                                                                                                        0.000175
## NewsAverage                                                                                                  0.000322
## log(NewsCount)                                                                                               0.000127
## log(Amihud_monthly)                                                                                          0.000185
## OMRFlag                                                                                                      0.000378
## l(RET_m1, 1)                                                                                                 0.000552
## l(RET_m1, 2)                                                                                                 0.000515
## l(RET_m1, 3)                                                                                                 0.000435
## log(TA)                                                                                                      0.000458
## CtA                                                                                                          0.000831
## EBITDAtA                                                                                                     0.004034
## Leverage                                                                                                     0.001629
## log(BM)                                                                                                      0.000148
## DivtoAsset                                                                                                   0.043006
## l(log(MarCap), 1)                                                                                            0.000438
##                                                                                                               t value
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::FALSE  -2.052763
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE   -1.657419
## l(RepIntensity, 1)                                                                                           6.254819
## log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE           -0.744495
## ANews                                                                                                       -1.480527
## NewsAverage                                                                                                  0.221083
## log(NewsCount)                                                                                              -0.642588
## log(Amihud_monthly)                                                                                        -11.021083
## OMRFlag                                                                                                      4.191416
## l(RET_m1, 1)                                                                                                -6.891972
## l(RET_m1, 2)                                                                                                -2.353632
## l(RET_m1, 3)                                                                                                -1.267371
## log(TA)                                                                                                     -2.137048
## CtA                                                                                                          2.447299
## EBITDAtA                                                                                                     1.111260
## Leverage                                                                                                     0.836809
## log(BM)                                                                                                      6.071381
## DivtoAsset                                                                                                   1.154227
## l(log(MarCap), 1)                                                                                           -2.244551
##                                                                                                              Pr(>|t|)
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::FALSE 4.0356e-02
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE  9.7749e-02
## l(RepIntensity, 1)                                                                                         5.8917e-10
## log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE          4.5675e-01
## ANews                                                                                                      1.3905e-01
## NewsAverage                                                                                                8.2507e-01
## log(NewsCount)                                                                                             5.2064e-01
## log(Amihud_monthly)                                                                                         < 2.2e-16
## OMRFlag                                                                                                    3.0178e-05
## l(RET_m1, 1)                                                                                               9.7331e-12
## l(RET_m1, 2)                                                                                               1.8784e-02
## l(RET_m1, 3)                                                                                               2.0532e-01
## log(TA)                                                                                                    3.2836e-02
## CtA                                                                                                        1.4564e-02
## EBITDAtA                                                                                                   2.6672e-01
## Leverage                                                                                                   4.0290e-01
## log(BM)                                                                                                    1.7992e-09
## DivtoAsset                                                                                                 2.4868e-01
## l(log(MarCap), 1)                                                                                          2.5015e-02
##                                                                                                               
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::FALSE *  
## fit_AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE  .  
## l(RepIntensity, 1)                                                                                         ***
## log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE             
## ANews                                                                                                         
## NewsAverage                                                                                                   
## log(NewsCount)                                                                                                
## log(Amihud_monthly)                                                                                        ***
## OMRFlag                                                                                                    ***
## l(RET_m1, 1)                                                                                               ***
## l(RET_m1, 2)                                                                                               *  
## l(RET_m1, 3)                                                                                                  
## log(TA)                                                                                                    *  
## CtA                                                                                                        *  
## EBITDAtA                                                                                                      
## Leverage                                                                                                      
## log(BM)                                                                                                    ***
## DivtoAsset                                                                                                    
## l(log(MarCap), 1)                                                                                          *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005039     Adj. R2: 0.238934
##                  Within R2: 0.053414
## F-test (1st stage), AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::FALSE: stat = 2,162.9     , p < 2.2e-16 , on 2 and 21,521 DoF.
## F-test (1st stage), AIA:log(1 + RET_m1) + f(log(1 + RET_m1), 1) + f(log(1 + RET_m1), 2) + f(log(1 + RET_m1), 3) > 0::TRUE : stat = 5,345.2     , p < 2.2e-16 , on 2 and 21,521 DoF.
##                                                                                                                 Wu-Hausman: stat =     0.350111, p = 0.704614, on 2 and 20,520 DoF.
fe_2sls_pQ <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(l(RET_m1, 1)>0) + 
                         # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                         ANews + NewsAverage + log(NewsCount) + 
                         log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                         # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                         # MarCap + Month + Volatility + TradeVol
                         l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                         l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                       | Ticker + time | # AIA ~ MarketAIA, 
                         # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                         # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                         # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                         # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
                         AIA:i(l(RET_m1, 1)>0) ~ MarketAIA:i(l(RET_m1, 1)>0), 
                       data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                       # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                       cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315, IV: 12,152/12,152).
fe_2sls_pQ
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:i(l(RET_m1, 1) > 0), Instr.: MarketAIA:i(l(RET_m1, 1) > 0)
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                                  Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA:l(RET_m1, 1) > 0::FALSE -0.000468   0.000257  -1.821376 6.8793e-02 .  
## fit_AIA:l(RET_m1, 1) > 0::TRUE  -0.000639   0.000208  -3.072069 2.1726e-03 ** 
## l(RepIntensity, 1)               0.175878   0.024351   7.222548 8.9271e-13 ***
## l(RET_m1, 1) > 0::TRUE           0.000036   0.000341   0.106678 9.1506e-01    
## ANews                           -0.000520   0.000155  -3.347018 8.4158e-04 ***
## NewsAverage                      0.000125   0.000346   0.362007 7.1741e-01    
## log(NewsCount)                   0.000109   0.000103   1.058184 2.9018e-01    
## log(Amihud_monthly)             -0.002069   0.000150 -13.775538  < 2.2e-16 ***
## OMRFlag                          0.001651   0.000297   5.552919 3.4404e-08 ***
## l(RET_m1, 1)                    -0.003740   0.000639  -5.851871 6.2287e-09 ***
## l(RET_m1, 2)                    -0.001547   0.000399  -3.878295 1.1077e-04 ***
## l(RET_m1, 3)                    -0.000562   0.000371  -1.514857 1.3007e-01    
## log(TA)                         -0.000851   0.000421  -2.021946 4.3398e-02 *  
## CtA                              0.001768   0.000763   2.317741 2.0627e-02 *  
## EBITDAtA                         0.004983   0.002835   1.757588 7.9067e-02 .  
## Leverage                         0.000124   0.001462   0.084876 9.3237e-01    
## log(BM)                          0.000945   0.000139   6.821462 1.4111e-11 ***
## DivtoAsset                      -0.008954   0.017970  -0.498287 6.1837e-01    
## l(log(MarCap), 1)               -0.001175   0.000386  -3.044529 2.3800e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005407     Adj. R2: 0.230476
##                  Within R2: 0.056576
## F-test (1st stage), AIA:l(RET_m1, 1) > 0::FALSE: stat = 4,905.4    , p < 2.2e-16 , on 2 and 39,349 DoF.
## F-test (1st stage), AIA:l(RET_m1, 1) > 0::TRUE : stat = 7,106.8    , p < 2.2e-16 , on 2 and 39,349 DoF.
##                                      Wu-Hausman: stat =     1.41418, p = 0.243137, on 2 and 38,119 DoF.
#### 7.1 with CAR 1-, 3- and 6-month  ====== 
pdShaRep %>% names
##  [1] "YM"               "AIAC"             "ANews"            "NewsAverage"     
##  [5] "NewsCount"        "MarketAIA"        "MarketAIAC"       "CUSIP"           
##  [9] "CIK"              "gvkey"            "Name"             "cusip8"          
## [13] "CUSIP_tts"        "AIA"              "ShaRep3"          "missing3"        
## [17] "Price2"           "Amihud_monthly"   "OMRFlag"          "Ticker"          
## [21] "RET_m1"           "Volatility"       "AvePrice"         "TradeVol"        
## [25] "TradeVolDollar"   "MarCap"           "ShaOut"           "ShaOutPrevious"  
## [29] "datadate"         "tic"              "cusip"            "atq"             
## [33] "ceqq"             "cheq"             "oibdpq"           "pstkq"           
## [37] "seqq"             "txditcq"          "cdvcy"            "costat"          
## [41] "dlcq"             "dlttq"            "BE"               "TD"              
## [45] "CtA"              "TA"               "Year"             "Quarter"         
## [49] "Month"            "RepIntensity"     "RepIntensity_vol" "ShaRepYes"       
## [53] "BM"               "DivtoAsset"       "EBITDA"           "Leverage"        
## [57] "TradeVol_scaled"  "EBITDAtA"         "time"             "sic"             
## [61] "shortintadj"      "OMR_YM"           "ProgramMonth"     "ShortInterest"   
## [65] "wv_bhar_reb3"     "wv_bhar_nreb3"    "wv_bhar_reb6"     "wv_bhar_nreb6"   
## [69] "wv_bhar_reb1"     "wv_bhar_nreb1"    "wv_bhar_reb0"     "wv_bhar_nreb0"   
## [73] "TradeVol_shaout"  "BM_q1"            "BM_q2"            "BM_q3"           
## [77] "BM_q4"            "RET_md"           "RET_mean"         "frequency"       
## [81] "Volatility_md"    "UnderPriced"      "BM_middle"        "PriceQ1"         
## [85] "PriceQ2"          "PriceQ3"          "PriceQ4"          "PriceQ"          
## [89] "HighVolatility"   "RET_m1_0"         "YQ"
fe_2sls_CARm3 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(wv_bhar_reb6 > 0) + # i((wv_bhar_reb6 > 0) + RET_m1_0) + # i(l(RET_m1 > RET_mean,-1)) + 
                               # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                               ANews + NewsAverage + log(NewsCount) + 
                               log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                               # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                               # MarCap + Month + Volatility + TradeVol
                               l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                               l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                             | Ticker + time | # AIA ~ MarketAIA, 
                               # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                               # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                               # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                               AIA:i(wv_bhar_reb6 > 0) ~ # i((wv_bhar_reb6 > 0) + RET_m1_0) ~ 
                               MarketAIA:i(wv_bhar_reb6 > 0) ,  # i((wv_bhar_reb6 > 0) + RET_m1_0) , 
                             # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                             data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                             # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                             cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 40,313 observations removed because of NA and infinite values (RHS: 40,313, IV: 14,523/14,523).
fe_2sls_CARm3
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: AIA:i(wv_bhar_reb6 > 0), Instr.: MarketAIA:i(wv_bhar_reb6 > 0)
## Second stage: Dep. Var.: RepIntensity
## Observations: 33,472 
## Fixed-effects: Ticker: 1,115,  time: 93
## Standard-errors: Clustered (Ticker) 
##                                  Estimate Std. Error    t value   Pr(>|t|)    
## fit_AIA:wv_bhar_reb6 > 0::FALSE -0.000883   0.000216  -4.085102 4.7212e-05 ***
## fit_AIA:wv_bhar_reb6 > 0::TRUE  -0.000285   0.000205  -1.386244 1.6595e-01    
## l(RepIntensity, 1)               0.161063   0.025194   6.392807 2.3905e-10 ***
## wv_bhar_reb6 > 0::TRUE          -0.000290   0.000294  -0.988318 3.2321e-01    
## ANews                           -0.000463   0.000170  -2.716348 6.7028e-03 ** 
## NewsAverage                      0.000083   0.000382   0.218290 8.2724e-01    
## log(NewsCount)                   0.000053   0.000106   0.494705 6.2091e-01    
## log(Amihud_monthly)             -0.002037   0.000161 -12.652363  < 2.2e-16 ***
## OMRFlag                          0.001631   0.000337   4.834446 1.5222e-06 ***
## l(RET_m1, 1)                    -0.004136   0.000501  -8.248340 4.4888e-16 ***
## l(RET_m1, 2)                    -0.001488   0.000426  -3.494269 4.9404e-04 ***
## l(RET_m1, 3)                    -0.000805   0.000435  -1.850430 6.4516e-02 .  
## log(TA)                         -0.001104   0.000451  -2.445751 1.4609e-02 *  
## CtA                              0.002000   0.000818   2.444367 1.4665e-02 *  
## EBITDAtA                         0.002166   0.002721   0.795720 4.2636e-01    
## Leverage                         0.000604   0.001552   0.389121 6.9726e-01    
## log(BM)                          0.001097   0.000171   6.414184 2.0884e-10 ***
## DivtoAsset                      -0.037533   0.024267  -1.546656 1.2223e-01    
## l(log(MarCap), 1)               -0.000869   0.000423  -2.054018 4.0207e-02 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.0053     Adj. R2: 0.225262
##                Within R2: 0.050838
## F-test (1st stage), AIA:wv_bhar_reb6 > 0::FALSE: stat = 4,985.5    , p < 2.2e-16, on 2 and 33,360 DoF.
## F-test (1st stage), AIA:wv_bhar_reb6 > 0::TRUE : stat = 6,194.8    , p < 2.2e-16, on 2 and 33,360 DoF.
##                                      Wu-Hausman: stat =     2.72349, p = 0.06566, on 2 and 32,244 DoF.
#### 7.11 Wald test. 
aod::wald.test(Sigma = fixest::vcov_cluster(fe_2sls_CARm3, cluster = c("Ticker")), b = fe_2sls_CARm3$coefficients, Terms = 1:2)
## Wald test:
## ----------
## 
## Chi-squared test:
## X2 = 29.6, df = 2, P(> X2) = 3.8e-07
{
  fe_2sls_CARm0 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(wv_bhar_reb0 > 0) + # i((wv_bhar_reb6 > 0) + RET_m1_0) + # i(l(RET_m1 > RET_mean,-1)) + 
                           # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                           ANews + NewsAverage + log(NewsCount) + 
                           log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                           # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                           # MarCap + Month + Volatility + TradeVol
                           l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                           l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                         | Ticker + time | # AIA ~ MarketAIA, 
                           # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                           # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                           # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                           AIA:i(wv_bhar_reb0 > 0) ~ # i((wv_bhar_reb6 > 0) + RET_m1_0) ~ 
                           MarketAIA:i(wv_bhar_reb0 > 0) ,  # i((wv_bhar_reb6 > 0) + RET_m1_0) , 
                         # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                         data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                         # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                         cluster = c("Ticker"))
  fe_2sls_CARm1 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(wv_bhar_reb1 > 0) + # i((wv_bhar_reb6 > 0) + RET_m1_0) + # i(l(RET_m1 > RET_mean,-1)) + 
                           # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                           ANews + NewsAverage + log(NewsCount) + 
                           log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                           # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                           # MarCap + Month + Volatility + TradeVol
                           l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                           l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                         | Ticker + time | # AIA ~ MarketAIA, 
                           # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                           # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                           # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                           AIA:i(wv_bhar_reb1 > 0) ~ # i((wv_bhar_reb6 > 0) + RET_m1_0) ~ 
                           MarketAIA:i(wv_bhar_reb1 > 0) ,  # i((wv_bhar_reb6 > 0) + RET_m1_0) , 
                         # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                         data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                         # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                         cluster = c("Ticker"))
  fe_2sls_CARm3 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(wv_bhar_reb3 > 0) + # i((wv_bhar_reb6 > 0) + RET_m1_0) + # i(l(RET_m1 > RET_mean,-1)) + 
                           # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                           ANews + NewsAverage + log(NewsCount) + 
                           log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                           # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                           # MarCap + Month + Volatility + TradeVol
                           l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                           l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                         | Ticker + time | # AIA ~ MarketAIA, 
                           # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                           # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                           # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                           AIA:i(wv_bhar_reb3 > 0) ~ # i((wv_bhar_reb6 > 0) + RET_m1_0) ~ 
                           MarketAIA:i(wv_bhar_reb3 > 0) ,  # i((wv_bhar_reb6 > 0) + RET_m1_0) , 
                         # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                         data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                         # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                         cluster = c("Ticker"))
  fe_2sls_CARm6 <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(wv_bhar_reb6 > 0) + # i((wv_bhar_reb6 > 0) + RET_m1_0) + # i(l(RET_m1 > RET_mean,-1)) + 
                           # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                           ANews + NewsAverage + log(NewsCount) + 
                           log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                           # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                           # MarCap + Month + Volatility + TradeVol
                           l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                           l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                         | Ticker + time | # AIA ~ MarketAIA, 
                           # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                           # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                           # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                           AIA:i(wv_bhar_reb6 > 0) ~ # i((wv_bhar_reb6 > 0) + RET_m1_0) ~ 
                           MarketAIA:i(wv_bhar_reb6 > 0) ,  # i((wv_bhar_reb6 > 0) + RET_m1_0) , 
                         # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                         data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                         # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                         cluster = c("Ticker"))
  
  etable(summary(fe_2sls_CARm0, stage = 2),
         summary(fe_2sls_CARm1, stage = 2),
         summary(fe_2sls_CARm3, stage = 2), 
         summary(fe_2sls_CARm6, stage = 2),
         fitstat = ~ . + ivfall + ivwaldall + wh + wh.p, 
         tex = T) 
}
## Warning in log(BM): NaNs produced
## NOTE: 40,362 observations removed because of NA and infinite values (RHS: 40,362, IV: 14,644/14,644).
## Warning in log(BM): NaNs produced
## NOTE: 40,313 observations removed because of NA and infinite values (RHS: 40,313, IV: 14,523/14,523).
## Warning in log(BM): NaNs produced
## NOTE: 40,313 observations removed because of NA and infinite values (RHS: 40,313, IV: 14,523/14,523).
## Warning in log(BM): NaNs produced
## NOTE: 40,313 observations removed because of NA and infinite values (RHS: 40,313, IV: 14,523/14,523).
## \begingroup
## \centering
## \begin{tabular}{lcccc}
##    \tabularnewline \midrule \midrule
##    Dependent Variable: & \multicolumn{4}{c}{RepIntensity}\\
##    Model:                        & (1)                   & (2)                    & (3)                   & (4)\\  
##    \midrule
##    \emph{Variables}\\
##    AIA:wv\_bhar\_reb0>0::FALSE   & -0.0009$^{***}$       &                        &                       &   \\   
##                                  & (0.0002)              &                        &                       &   \\   
##    AIA:wv\_bhar\_reb0>0::TRUE    & -0.0002               &                        &                       &   \\   
##                                  & (0.0002)              &                        &                       &   \\   
##    l(RepIntensity,1)             & 0.1611$^{***}$        & 0.1611$^{***}$         & 0.1609$^{***}$        & 0.1611$^{***}$\\   
##                                  & (0.0252)              & (0.0252)               & (0.0252)              & (0.0252)\\   
##    wv\_bhar\_reb0>0 $=$ TRUE     & -0.0007$^{**}$        &                        &                       &   \\   
##                                  & (0.0003)              &                        &                       &   \\   
##    ANews                         & -0.0005$^{***}$       & -0.0005$^{***}$        & -0.0005$^{***}$       & -0.0005$^{***}$\\   
##                                  & (0.0002)              & (0.0002)               & (0.0002)              & (0.0002)\\   
##    NewsAverage                   & $8.56\times 10^{-5}$  & 0.0001                 & $7.48\times 10^{-5}$  & $8.34\times 10^{-5}$\\    
##                                  & (0.0004)              & (0.0004)               & (0.0004)              & (0.0004)\\   
##    log(NewsCount)                & $5.26\times 10^{-5}$  & $4.57\times 10^{-5}$   & $5.45\times 10^{-5}$  & $5.26\times 10^{-5}$\\    
##                                  & (0.0001)              & (0.0001)               & (0.0001)              & (0.0001)\\   
##    log(Amihud\_monthly)          & -0.0021$^{***}$       & -0.0021$^{***}$        & -0.0021$^{***}$       & -0.0020$^{***}$\\   
##                                  & (0.0002)              & (0.0002)               & (0.0002)              & (0.0002)\\   
##    OMRFlag                       & 0.0016$^{***}$        & 0.0016$^{***}$         & 0.0016$^{***}$        & 0.0016$^{***}$\\   
##                                  & (0.0003)              & (0.0003)               & (0.0003)              & (0.0003)\\   
##    l(RET\_m1,1)                  & -0.0043$^{***}$       & -0.0041$^{***}$        & -0.0041$^{***}$       & -0.0041$^{***}$\\   
##                                  & (0.0005)              & (0.0005)               & (0.0005)              & (0.0005)\\   
##    l(RET\_m1,2)                  & -0.0015$^{***}$       & -0.0015$^{***}$        & -0.0015$^{***}$       & -0.0015$^{***}$\\   
##                                  & (0.0004)              & (0.0004)               & (0.0004)              & (0.0004)\\   
##    l(RET\_m1,3)                  & -0.0008$^{*}$         & -0.0008$^{*}$          & -0.0008$^{*}$         & -0.0008$^{*}$\\   
##                                  & (0.0004)              & (0.0004)               & (0.0004)              & (0.0004)\\   
##    log(TA)                       & -0.0009$^{*}$         & -0.0011$^{**}$         & -0.0011$^{**}$        & -0.0011$^{**}$\\   
##                                  & (0.0005)              & (0.0005)               & (0.0005)              & (0.0005)\\   
##    CtA                           & 0.0020$^{**}$         & 0.0020$^{**}$          & 0.0020$^{**}$         & 0.0020$^{**}$\\   
##                                  & (0.0008)              & (0.0008)               & (0.0008)              & (0.0008)\\   
##    EBITDAtA                      & 0.0024                & 0.0021                 & 0.0022                & 0.0022\\   
##                                  & (0.0027)              & (0.0027)               & (0.0027)              & (0.0027)\\   
##    Leverage                      & $-9.5\times 10^{-5}$  & 0.0008                 & 0.0008                & 0.0006\\   
##                                  & (0.0016)              & (0.0016)               & (0.0016)              & (0.0016)\\   
##    log(BM)                       & 0.0010$^{***}$        & 0.0011$^{***}$         & 0.0011$^{***}$        & 0.0011$^{***}$\\   
##                                  & (0.0002)              & (0.0002)               & (0.0002)              & (0.0002)\\   
##    DivtoAsset                    & -0.0394               & -0.0388                & -0.0389$^{*}$         & -0.0375\\   
##                                  & (0.0244)              & (0.0242)               & (0.0235)              & (0.0243)\\   
##    l(log(MarCap),1)              & -0.0012$^{***}$       & -0.0009$^{**}$         & -0.0009$^{**}$        & -0.0009$^{**}$\\   
##                                  & (0.0004)              & (0.0004)               & (0.0004)              & (0.0004)\\   
##    AIA:wv\_bhar\_reb1>0::FALSE   &                       & -0.0007$^{***}$        &                       &   \\   
##                                  &                       & (0.0002)               &                       &   \\   
##    AIA:wv\_bhar\_reb1>0::TRUE    &                       & -0.0005$^{**}$         &                       &   \\   
##                                  &                       & (0.0002)               &                       &   \\   
##    wv\_bhar\_reb1>0 $=$ TRUE     &                       & $-9.11\times 10^{-5}$  &                       &   \\   
##                                  &                       & (0.0003)               &                       &   \\   
##    AIA:wv\_bhar\_reb3>0::FALSE   &                       &                        & -0.0009$^{***}$       &   \\   
##                                  &                       &                        & (0.0002)              &   \\   
##    AIA:wv\_bhar\_reb3>0::TRUE    &                       &                        & -0.0003               &   \\   
##                                  &                       &                        & (0.0002)              &   \\   
##    wv\_bhar\_reb3>0 $=$ TRUE     &                       &                        & -0.0003               &   \\   
##                                  &                       &                        & (0.0003)              &   \\   
##    AIA:wv\_bhar\_reb6>0::FALSE   &                       &                        &                       & -0.0009$^{***}$\\   
##                                  &                       &                        &                       & (0.0002)\\   
##    AIA:wv\_bhar\_reb6>0::TRUE    &                       &                        &                       & -0.0003\\   
##                                  &                       &                        &                       & (0.0002)\\   
##    wv\_bhar\_reb6>0 $=$ TRUE     &                       &                        &                       & -0.0003\\   
##                                  &                       &                        &                       & (0.0003)\\   
##    \midrule
##    \emph{Fixed-effects}\\
##    Ticker                        & Yes                   & Yes                    & Yes                   & Yes\\  
##    time                          & Yes                   & Yes                    & Yes                   & Yes\\  
##    \midrule
##    \emph{Fit statistics}\\
##    Observations                  & 33,423                & 33,472                 & 33,472                & 33,472\\  
##    R$^2$                         & 0.25368               & 0.25507                & 0.25370               & 0.25362\\  
##    Within R$^2$                  & 0.05106               & 0.05269                & 0.05095               & 0.05084\\  
##    F-test (IV only)              & 24.002                & 21.895                 & 23.341                & 23.192\\  
##    Wald (IV only)                & 14.504                & 13.247                 & 13.842                & 14.790\\  
##    Wu-Hausman                    & 2.4000                & 0.56867                & 2.5708                & 2.7235\\  
##    Wu-Hausman, p-value           & 0.09074               & 0.56628                & 0.07649               & 0.06566\\  
##    \midrule \midrule
##    \multicolumn{5}{l}{\emph{Clustered (Ticker) standard-errors in parentheses}}\\
##    \multicolumn{5}{l}{\emph{Signif. Codes: ***: 0.01, **: 0.05, *: 0.1}}\\
## \end{tabular}
## \par\endgroup
if (0 == 1) {
  
fe_2sls_CARm3_extra <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + i(group6) + # i((wv_bhar_reb6 > 0) + RET_m1_0) + # i(l(RET_m1 > RET_mean,-1)) + 
                         # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                         ANews + NewsAverage + log(NewsCount) + 
                         log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
                         # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                         # MarCap + Month + Volatility + TradeVol
                         l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
                         l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
                       | Ticker + time | # AIA ~ MarketAIA, 
                         # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
                         # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
                         # AIA:l(1-ShaRepYes, 1, fill = NA) + AIA:l(ShaRepYes, 1, fill = NA) ~ MarketAIA:l(1-ShaRepYes, 1, fill = NA) + MarketAIA:l(ShaRepYes, 1, fill = NA) , 
                         AIA:i(group6) ~ # i((wv_bhar_reb6 > 0) + RET_m1_0) ~ 
                         MarketAIA:i(group6),  # i((wv_bhar_reb6 > 0) + RET_m1_0) , 
                       # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
                       data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
                       # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
                       cluster = c("Ticker"))
fe_2sls_CARm3_extra
summary(fe_2sls_CARm3_extra, stage = 2)

ggplot(data = data.frame(pdShaRep)) + 
  geom_histogram(aes(x = group1)) + 
  geom_histogram(aes(x = group3)) + 
  geom_histogram(aes(x = group6)) 
}

feols(fml = RepIntensity ~ AIA:i(l(ShaRepYes, 1, fill = NA)) + l(RepIntensity, 1) + 
        # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
        ANews + NewsAverage + log(NewsCount) + 
        log(Amihud_monthly) + l(OMRFlag, 0, fill = 0) + # log(1 + NewsCount) +
        # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
        # MarCap + Month + Volatility + TradeVol
        l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) + 
        l(log(MarCap), 1) # + d(Volatility,1) + l(Volatility, 1) + (TradeVol_scaled) # + lambda
      | Ticker + time, # | # AIA ~ MarketAIA, 
        # AIA ~ MarketAIA, #  + Ticker^yearqtr(YM) 
        # AIA:(1-UnderPriced) + AIA:UnderPriced ~ MarketAIA:(1-UnderPriced) + MarketAIA:UnderPriced, ## UnderPriced versus Overpriced 
        #  ~ MarketAIA:l(1-ShaRepYes, 1, fill = 0) + MarketAIA:l(ShaRepYes, 1, fill = 0) , 
      # AIA:i(l(RET_m1,-1) > 0) ~ MarketAIA:i(l(RET_m1,-1) > 0), 
      # AIA:i(l(log(1 + RET_m1),-1:-3) > 0) ~ MarketAIA:i(l(log(1 + RET_m1),-1:-3) > 0), 
      data = pdShaRep, #[pdShaRep$ShaRepYes == T,], 
      # data = pdShaRep[pdShaRep$RepIntensity > 0,], 
      cluster = c("Ticker")) # %>% 
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315).
## OLS estimation, Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## l(RepIntensity, 1)   0.164397   0.025268   6.506190 1.1197e-10 ***
## ANews               -0.000513   0.000156  -3.293381 1.0181e-03 ** 
## NewsAverage          0.000042   0.000348   0.119814 9.0465e-01    
## log(NewsCount)       0.000130   0.000101   1.284798 1.9911e-01    
## log(Amihud_monthly) -0.002084   0.000149 -13.955516  < 2.2e-16 ***
## OMRFlag              0.001617   0.000296   5.457706 5.8301e-08 ***
## l(RET_m1, 1)        -0.003997   0.000475  -8.415691  < 2.2e-16 ***
## l(RET_m1, 2)        -0.001542   0.000397  -3.887928 1.0651e-04 ***
## ... 10 coefficients remaining (display them with summary() or use argument n)
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.005402     Adj. R2: 0.232004
##                  Within R2: 0.058425
  # su <- ary()

#### 8. falsification test for the exclusive restriction ----
### 8.1 use the last AIA 
fe_2sls_exclusiveres <- feols(fml = RepIntensity ~ l(RepIntensity, 1) + 
                   # l(ANews, 0) + l(log(1+NewsAverage), 0) + l(log(1+NewsCount), 0) + 
                   ANews + NewsAverage + log(NewsCount) + 
                   log(Amihud_monthly) + OMRFlag + # log(1 + NewsCount) +
                   # RET_m1 + TA + CtA + (EBITDA/TA) + Leverage + BM + DivtoAsset + 
                   # MarCap + Month + Volatility + TradeVol
                   l(RET_m1, 1:3)+ log(TA) + (CtA) + (EBITDAtA) + (Leverage) + log(BM) + (DivtoAsset) +   
                   l(log(MarCap), 1) # + ShortInterest + d(ShortInterest,1) # + d(Volatility,1) + l(Volatility, 1) + TradeVol_scaled # + lambda
                 | Ticker + time | l(AIA,1) ~ l(MarketAIA,1), # + Ticker^yearqtr(YM) # + Ticker^YQ
                 data = pdShaRep, # [pdShaRep$AIA < 4.0,], # [pdShaRep$RepIntensity > 0,], 
                 cluster = c("Ticker"))
## Warning in log(BM): NaNs produced
## NOTE: 34,315 observations removed because of NA and infinite values (RHS: 34,315, IV: 12,149/12,149).
summary(fe_2sls_exclusiveres, stage = 1:2)
## IV: First stage: l(AIA, 1)
## TSLS estimation, Dep. Var.: l(AIA, 1), Endo.: l(AIA, 1), Instr.: l(MarketAIA, 1)
## First stage: Dep. Var.: l(AIA, 1)
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                         Estimate Std. Error     t value  Pr(>|t|)    
## l(MarketAIA, 1)     -1257.454989   4.589444 -273.988495 < 2.2e-16 ***
## l(RepIntensity, 1)     -0.203196   0.094104   -2.159273  0.031022 *  
## ANews                   0.005331   0.003466    1.538051  0.124294    
## NewsAverage            -0.015143   0.006328   -2.393021  0.016860 *  
## log(NewsCount)          0.005352   0.002305    2.322528  0.020367 *  
## log(Amihud_monthly)    -0.007360   0.003488   -2.109889  0.035070 *  
## OMRFlag                 0.000454   0.002938    0.154369  0.877344    
## l(RET_m1, 1)           -0.006768   0.008759   -0.772685  0.439858    
## l(RET_m1, 2)           -0.011056   0.007643   -1.446601  0.148264    
## l(RET_m1, 3)            0.000686   0.008374    0.081932  0.934714    
## log(TA)                 0.005039   0.010472    0.481180  0.630474    
## CtA                    -0.015659   0.018446   -0.848878  0.396115    
## EBITDAtA                0.094871   0.037581    2.524409  0.011715 *  
## Leverage               -0.042912   0.035337   -1.214348  0.224849    
## log(BM)                -0.001865   0.002661   -0.701040  0.483411    
## DivtoAsset             -0.323973   0.495359   -0.654015  0.513224    
## l(log(MarCap), 1)      -0.012468   0.008544   -1.459237  0.144756    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.141173     Adj. R2: 0.958238
##                  Within R2: 0.87927 
## F-test (1st stage): stat = 273,150.5, p < 2.2e-16, on 1 and 39,351 DoF.
## 
## IV: Second stage
## TSLS estimation, Dep. Var.: RepIntensity, Endo.: l(AIA, 1), Instr.: l(MarketAIA, 1)
## Second stage: Dep. Var.: RepIntensity
## Observations: 39,470 
## Fixed-effects: Ticker: 1,229,  time: 102
## Standard-errors: Clustered (Ticker) 
##                      Estimate Std. Error    t value   Pr(>|t|)    
## fit_l(AIA, 1)        0.000108   0.000098   1.108937 2.6767e-01    
## l(RepIntensity, 1)   0.176311   0.024416   7.221222 9.0110e-13 ***
## ANews               -0.000552   0.000157  -3.523424 4.4166e-04 ***
## NewsAverage         -0.000125   0.000353  -0.352920 7.2421e-01    
## log(NewsCount)       0.000027   0.000100   0.265088 7.9099e-01    
## log(Amihud_monthly) -0.002050   0.000150 -13.663296  < 2.2e-16 ***
## OMRFlag              0.001637   0.000297   5.509241 4.3866e-08 ***
## l(RET_m1, 1)        -0.003929   0.000475  -8.264944 3.5887e-16 ***
## l(RET_m1, 2)        -0.001536   0.000397  -3.863908 1.1742e-04 ***
## l(RET_m1, 3)        -0.000546   0.000373  -1.463218 1.4366e-01    
## log(TA)             -0.000858   0.000424  -2.024575 4.3127e-02 *  
## CtA                  0.001674   0.000755   2.216749 2.6823e-02 *  
## EBITDAtA             0.005156   0.002813   1.832958 6.7051e-02 .  
## Leverage            -0.000084   0.001466  -0.057275 9.5434e-01    
## log(BM)              0.000937   0.000139   6.727464 2.6407e-11 ***
## DivtoAsset          -0.009019   0.017976  -0.501724 6.1595e-01    
## l(log(MarCap), 1)   -0.001235   0.000389  -3.174696 1.5372e-03 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## RMSE: 0.00541     Adj. R2: 0.229841
##                 Within R2: 0.055749
## F-test (1st stage), l(AIA, 1): stat = 273,150.5    , p < 2.2e-16 , on 1 and 39,351 DoF.
##                    Wu-Hausman: stat =       1.38e-4, p = 0.990627, on 1 and 38,122 DoF.